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Global well-posedness and large time behavior for the inviscid Oldroyd-B model Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-03-11 Weikui Ye, Bin Zhao
In this paper, we consider the 3-dimensional incompressible inviscid Oldroyd-B model. Firstly, we establish the global existence of the solutions for the inviscid Oldroyd-B model with different coupling coefficient . Then, we show the connection between the solution with the parameter that is the reciprocal of Weissenberg number. On one hand, we prove that the solutions depend continuously on the parameter
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An upper bound for the number of small-amplitude limit cycles in non-smooth Liénard system Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-03-10 H, o, n, g, w, e, i, , S, h, i
The non-smooth Liénard system, a well-known nonlinear model, appears in a natural way in physics, chemistry, biology, and so on, in which periodic phenomena play a relevant role. In this paper, we investigate the small-amplitude limit cycles generated by the Hopf bifurcation of the non-smooth Liénard system. By utilizing the Picard–Fuchs equation, we gain the upper bounds of the number of small-amplitude
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Analysis of a nonlinear model for the thermoelastic beam Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-03-09 C. Cunha, M.R. Clark
This paper addresses the Cauchy problem associated with the nonlinear thermoelastic beam featuring thermal dissipation. We examine the problem in an open domain, which may be either bounded or unbounded. The existence of a solution is derived through the diagonalization theorem for self-adjoint operators using Hilbertian integral theory.
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The Cauchy problem for an inviscid and non-diffusive Oldroyd-B model in two dimensions Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-03-05 Yuanzhi Tu, Yinghui Wang, Huanyao Wen
A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by Elgindi and Rousset (2015) where the global existence and uniqueness of the strong solution were established for arbitrarily large initial data. As pointed out by Bhave et al. (1991), since the diffusion coefficient is significantly smaller than other effects, it is interesting to study the non-diffusive model. In the present
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Asymptotics for a wave equation with critical exponential nonlinearity Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-03-01 Tahir Boudjeriou, Nguyen Van Thin
In this paper, we discuss some qualitative analysis of solutions to the following Cauchy problem of wave equations involving the -Laplace operator with critical exponential nonlinearity where , , , and . By using the contraction mapping principle, we show that the above Cauchy problem has a unique local solution. With the help of the potential well argument, we characterize the stable sets by the asymptotic
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Dynamics of a mathematical model of virus spreading incorporating the effect of a vaccine Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-24 Aytül Gökçe, Burcu Gürbüz, Alan D. Rendall
The COVID-19 pandemic led to widespread interest in epidemiological models. In this context the role of vaccination in influencing the spreading of the disease is of particular interest. There has also been a lot of debate on the role of non-pharmaceutical interventions such as the disinfection of surfaces. We investigate a mathematical model for the spread of a disease which includes both imperfect
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Global well-posedness of Chemotaxis-Navier–Stokes system with refined rough initial data in Rd Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-24 Long Lin, Chenyin Qian
We consider the global solvability of the incompressible Chemotaxis-Navier–Stokes system in . We first investigate the global well-posedness of Chemotaxis-Navier–Stokes equations in by involving a double exponential function of the initial velocity field and the initial chemical concentration . By only giving the smallness assumption of initial cell density and the horizontal components of velocity
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Global energy conservation solution for the N−abc family of Camassa–Holm type equation Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-23 Zaiyun Zhang, Zhenhai Liu, Youjun Deng
In this paper, we investigate the family of Camassa–Holm type equation with -order nonlinearities. This quasi-linear equation is nonlocal with higher order nonlinearities, compared to the Camassa–Holm equation () and Novikov equation (). Using both the lower order and the higher order energy conservation laws, as well as the characteristic method, we establish the global existence and uniqueness of
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Global well-posedness and decay estimates for the one-dimensional models of blood flow with a general parabolic velocity profile Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-23 Fan Yang, Xiongfeng Yang
In this paper, we study the one-dimensional models of blood flow arising from the hemodynamics of aorta, which are derived from the averaging of the Navier–Stokes equations. We establish the global well-posedness and long-time behavior of the viscid 1D models of blood flow in the Sobolev space framework, where a general parabolic velocity profile is considered. Precisely speaking, we prove the global
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Weakly nonlinear analysis of a two-species non-local advection–diffusion system Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-23 Valeria Giunta, Thomas Hillen, Mark A. Lewis, Jonathan R. Potts
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection–diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of the constant steady state, then weakly nonlinear analysis
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Qualitative analysis of smooth solution for the Euler equations of Chaplygin gas Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-22 Xinglong Wu, Boling Guo
This manuscript is devoted to studying the blow-up phenomena and instability of the smooth solution for the isentropic Chaplygin gas equations in for any dimension . We first give two blow-up phenomena of the Chaplygin gas equations, if the initial data satisfy some conditions (compact support or spherical symmetry). Next, the dynamics and instability of a family of solutions for the Cauchy problem
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Rigorous estimates for the quasi-steady state approximation of the Michaelis–Menten reaction mechanism at low enzyme concentrations Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-19 Justin Eilertsen, Santiago Schnell, Sebastian Walcher
There is a vast amount of literature concerning the appropriateness of various perturbation parameters for the standard quasi-steady state approximation in the Michaelis–Menten reaction mechanism, and also concerning the relevance of these parameters for the accuracy of the approximation by the familiar Michaelis–Menten equation. Typically, the arguments in the literature are based on (heuristic) timescale
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Convergence of a double step scheme for a class of second order Clarke subdifferential inclusions Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-19 Krzysztof Bartosz, Paweł Szafraniec
In this paper we deal with a second order evolution inclusion involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a double step time-semidiscrete approximation, known as the Rothe scheme. We study a sequence of solutions of the semidiscrete approximate problems and provide its weak convergence to a limit element that is
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Global well-posedness and vanishing parameters limits for the systems of ferrohydrodynamics Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-19 Chuangen Xie
This paper is concerned with the systems modeling the dynamics of incompressible viscous ferrofluids. We first consider the Rosensweig system, which consists of the Navier–Stokes equations, the angular momentum equations, the magnetization equations and the magnetostatic equations. We prove the global existence and optimal time-decay rates of the unique strong solution to the Cauchy problem for the
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Rotation number and eigenvalues of two-component modified Camassa–Holm equations Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-18 Ke Jiang, Gang Meng, Zhi Zhang
In this paper, we study the spectral problem for the two-component modified Camassa–Holm equation, where are two potentials. By introducing the rotation number and studying its properties, we prove that for any integer , the periodic or anti-periodic eigenvalues are the endpoints of the interval . Moreover, we prove that as nonlinear functionals of potentials, such eigenvalues are continuous in potentials
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Threshold dynamics of a vector-bias malaria model with time-varying delays in environments of almost periodicity Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-16 Bing He, Qi-Ru Wang
A malaria transmission model having vector bias and time-dependent delays in environments of almost periodicity is considered. The basic reproduction ratio is presented, and the threshold dynamic is characterized by . By using the theories of skew-product semiflows, chain transitive sets, and subhomogeneous and monotone systems, it is proved that the model has only one positive almost periodic solution
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Bifurcation and stability of a reaction–diffusion–advection model with nonlocal delay effect and nonlinear boundary condition Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-15 Chaochao Li, Shangjiang Guo
In this paper, a reaction–diffusion–advection model with nonlocal delay effect and nonlinear boundary condition is investigated. By employing the Lyapunov–Schmidt reduction method, we not only establish the existence, multiplicity and stability of spatially nonhomogeneous steady-state solutions, but also obtain some sufficient conditions ensuring the occurrence of a Hopf bifurcation at the steady-state
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Lyapunov stability of the Einstein–Friedmann dynamical equations of barotropic FRW cosmologies Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-13 Zaitao Liang, Feng Wang, Nana Xie
In this paper, we investigate the Einstein–Friedmann dynamical equations of barotropic Friedmann–Robertson–Walker (FRW) cosmologies, taking into account the time-varying energy density and pressure. Based on the third-order approximation method, the upper–lower solutions method and some quantitative analysis, we establish some sufficient conditions for the Lyapunov stability of periodic solutions.
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The critical mass curve and chemotactic collapse of a two-species chemotaxis system with two chemicals Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-07 Hao Yu, Bingqian Xue, YinYin Hu, Lifen Zhao
This paper considers the following two-species chemotaxis system with two chemicals subject to the homogeneous Neumann boundary condition with , where is a smooth bounded domain. In the previous paper [Yu et al, Criteria on global boundedness versus finite time blow-up to a two-species chemotaxis system with two chemicals, Nonlinearity 31 (2018) 502–514], we proved that the system possesses finite-time
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Agent-based pattern formation in a chemostat system with asymmetric dispersal Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-07 Quanen Wu, Yuanshi Wang, Shikun Wang, Hong Wu
An agent-based chemostat system is considered, where there exist a resource and a consumer. Each individual of the consumer acts as an agent, which moves between patches on a plane and asymmetry in the dispersal is driven by resources in the nearest-neighbor patches. Based on laboratory experiments and the corresponding models by Zhang et al. (2020), we propose an agent-based model to characterize
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Sufficient conditions for the existence of minimizing harmonic maps with axial symmetry in the small-average regime Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-06 Giovanni Di Fratta, Valeriy V. Slastikov, Arghir D. Zarnescu
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields , where and are surfaces of revolution. The energy functional we consider is closely related to a reduced model in the variational theory of micromagnetism for the analysis of observable magnetization states in curved thin films. We show that axially symmetric minimizers
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Global well-posedness for a family of regularized Benjamin-type equations Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-06 Izabela Patricio Bastos, Daniel G. Alfaro Vigo, Ailin Ruiz de Zarate Fabregas, Janaina Schoeffel, César J. Niche
In this work we prove local and global well-posedness results for the Cauchy problem of a family of regularized nonlinear Benjamin-type equations in both periodic and nonperiodic Sobolev spaces.
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On the five Lagrange points in a generalized surface quasi-geostrophic flow Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-02 Mei Zhang, Changjun Zou
We consider rotating solutions of the generalized surface quasi-geostrophic (gSQG) equation, and prove the existence of five relative stationary points, namely, the Lagrange points near a co-rotating point vortex pair. We also construct a branch of solutions locally bifurcating from the point vortex pair, which consist of a regular vortex pair and several point vortices located near those Lagrange
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Global weak solutions in a singular taxis-type system with signal consumption Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-30 Zhen Chen, Genglin Li
Relevant to modeling starvation-driven species dispersal is the chemotaxis-consumption system, featuring singular signal-dependent motilities, given by ut=Δ(umv−α),vt=Δv−uv,which is considered under homogeneous boundary conditions in smoothly bounded domains Ω⊂Rn, n≥1, with m>1 and α>0. In the context of concurrent strengthening of diffusion and cross-diffusion in the first equation of this system
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On the vanishing viscosity limit for 3D axisymmetric flows without swirl Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-02-01 Patrick Brkic, Emil Wiedemann
We study the vanishing viscosity limit for the three-dimensional incompressible Navier–Stokes equations in terms of the relative vorticity in the setting of axisymmetric velocity fields without swirl. We show that the weak convergence of relative vorticity to a renormalized solution of the Euler equations, established by Nobili and Seis, can be upgraded to strong convergence.
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Wave speeds in delayed diffusion equations with ignition and degenerate nonlinearities Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-25 Wei-Jian Bo, Guo Lin
This article explores the factors that affect the unique wave speed in delayed ignition equation and the minimal wave speed in delayed degenerate equation. In the ignition case, it is proved that the unique wave speed is strictly decreasing and continuous with respect to the delay and ignition temperature, respectively. Under the degenerate case, by a class of auxiliary equations and the detailed asymptotic
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A HANDY-type model with non renewable resources Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-25 M. Badiale, I. Cravero
In this paper we study a modified HANDY model, describing interactions between nature resources and human exploitation. It is a system of four ODEs, whose vector field is non differentiable at certain points. The main novelty of our approach is the introduction of a variable describing non renewable resources, whose equation contains both a consumption and a replenishment term. We first establish the
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Analysis of a degenerate reaction–diffusion anthrax model with spatial heterogeneity Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-22 Jin-Shan Wang, Hongyong Zhao
To investigate the impact of spatial heterogeneity on anthrax transmission, we develop a novel degenerate reaction–diffusion model for anthrax. Despite the lack of compactness of the solution map, the asymptotic smoothness is confirmed by examining its contractility. We establish two thresholds, s(J) obtained by an auxiliary system and R0 defined by next generation operator, corresponding to the extinction
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Stability of the Couette flow for the two dimensional Chemotaxis-Navier–Stokes system Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-09 Dandan Ding, Zhong Tan
In this paper, we consider the stability of the Couette flow for the Cauchy problem to the parabolic-parabolic chemotaxis-Navier–Stokes system in T×R, we prove that the Couette flow is stable under the extra smallness assumption, where the amplitude is large enough. This result was inspired by Zeng et al. (2021), they investigated the suppression of blow-up in Patlak–Keller–Segel-Navier–Stokes system
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Energy equality of weak solutions of the Navier–Stokes–Fourier equations allowing vacuum Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-11 Xiang Ji, Shu Wang, Jie Zhang
In this paper, we are concerned with the conservation of energy criterion of the weak solutions to the Navier–Stokes–Fourier equations on the torus allowing vacuum. We establish the energy conservation criteria via the gradient of velocity for the weak solutions of this system, which generalizes the corresponding recent energy conservation criteria in terms of the velocity obtained by Aoki and Iwabuchi
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Improved algebraic lower bound for the radius of spatial analyticity for the generalized KdV equation Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-08 Mikaela Baldasso, Mahendra Panthee
We consider the initial value problem (IVP) for the generalized Korteweg–de Vries (gKdV) equation ∂tu+∂x3u+μuk∂xu=0,x∈R,t∈R,u(x,0)=u0(x),where u(x,t) is a real valued function, u0(x) is a real analytic function, μ=±1 and k≥4. We prove that if the initial data u0 has radius of analyticity σ0, then there exists T0>0 such that the radius of spatial analyticity of the solution remains the same in the time
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On small-data solution of the chemotaxis–SIS epidemic system with bilinear incidence rate Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-05 Qingshan Zhang
This paper deals with the initial–boundary value problem for chemotaxis susceptible-infected-susceptible epidemic system with bilinear incidence rate ut=d1Δu+χ∇⋅(u∇v)−β(x)uv+γ(x)v,x∈Ω,t>0,vt=d2Δv+β(x)uv−γ(x)v,x∈Ω,t>0 under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂Rn (n≥1), where d1>0, d2>0, χ∈R, 0<β∈C1(Ω¯) and 0<γ∈C1(Ω¯). It is proved that if (u(x,0),v(x,0)) in L∞(Ω)×L1(Ω)
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Dynamical behaviors of a specialist predator–prey system in open advective heterogeneous environments Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-05 Qi Wang
In this paper, we investigate the effect of dispersal and advection on the dynamics of a specialist predator–prey model. More precisely, we show that the linear stability of the semi-trivial steady state is determined by the dispersal rate, the mortality rate of the predator and the advection rate. We point out that compared to homogeneous intrinsic growth rate and carrying capacity, the case in this
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Second-order differential inclusions with two small parameters Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-05 Luminiţa Barbu, Gheorghe Moroşanu, Ioan Vladimir Vîntu
Consider in a real Hilbert space H the following problem, denoted (Pɛμ), −ɛu′′(t)+μu′(t)+Au(t)+Bu(t)∋f(t),00 is a given time instant, ɛ>0, μ≥0 are small parameters, A:D(A)⊂H→H is a maximal monotone operator (possibly multivalued), and B:H→H is a Lipschitz operator (or monotone and Lipschitz on bounded sets). Consider also the following reduced problem, denoted (Pμ), μu′(t)+Au(t)+Bu(t)∋f(t),00, as well
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Temperature dependent extensions of the Cahn–Hilliard equation Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-05 Francesco De Anna, Chun Liu, Anja Schlömerkemper, Jan-Eric Sulzbach
The Cahn–Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In this paper we focus on the dynamics of these binary media, when the underlying temperature is not constant. The aim of this paper is twofold. We first derive two distinct models that extend the classical Cahn-Hilliard equation with an evolutionary equation for the absolute temperature
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Population dynamics in a reaction–diffusion-advection predator–prey model with Beddington–DeAngelis functional response Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-02 Genjiao Zhou, Li Ma, Yin Wang
In this paper, we consider a two-species predator–prey model in advective heterogeneous environments with the Beddington–DeAngelis interaction term, where the Danckwerts boundary conditions are imposed. Applying the comparison principle for predator–prey system and persistence theory, we draw a clear picture on the long-time dynamics, which also indicates the existence and non-existence of the coexistence
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On second order differential inclusion driven by quasi-variational–hemivariational inequalities Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-03 Yunshui Liang, Lu-Chuan Ceng, Jen-Chih Yao, Shengda Zeng
In this paper we investigate an evolution problem (SDQHVI) which constitutes of the second order differential inclusion driven by a quasi-variational–hemivariational inequality (QHVI) with perturbation operator in Banach spaces. Unlike the existing literature on differential inclusions, on the one hand, the second order differential operator is not assumed to be compact; on the other hand, the solvability
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Monostable pulsating traveling waves in discrete periodic media with delay Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-03 Haiqin Zhao, Shi-Liang Wu, Xue Xue
The purpose of this article is to investigate various qualitative properties of pulsating traveling waves for a delayed lattice dynamical system with global interaction in periodic habitat. Under some appropriate assumptions, we first establish a Harnack type of inequality for its wave profile system. Then, we show that all wave profiles remain strictly increasing in the propagation process. Based
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Estimates on the velocity of a rigid body moving in a fluid Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2024-01-04 Stathis Filippas, Alkis Tersenov
We obtain estimates of all components of the velocity of a 3D rigid body moving in a viscous incompressible fluid without any symmetry restriction on the shape of the rigid body or the container. The estimates are in terms of suitable norms of the velocity field in a small domain of the fluid only, provided the distance h between the rigid body and the container is small. As a consequence we obtain
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Optimal decay rate of the incompressible Navier–Stokes–Maxwell system with Ohm’s law Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-12-26 Shuxian Tan, Fujun Zhou, Weijun Wu, Weihua Gong
This work is to establish optimal time decay rate of global classical solutions to the two-fluid incompressible Navier–Stokes–Maxwell system with Ohm’s law and the incompressible Navier–Stokes–Maxwell system with Ohm’s law in R3. The results show that the optimal time decay rate for the velocity of these two systems achieves the same as that of the incompressible Navier–Stokes equation. In other words
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Periodic solutions of a population dynamics model with hysteresis Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-12-07 Sergey A. Timoshin, Yifu Wang
This paper is concerned with a population dynamics model describing the evolution of three biological species. Our system takes into account diffusion and hysteretic effects underlying the evolution process. It is shown that the problem admits a time periodic solution under fairly general assumptions on the hysteresis region and right-hand sides of the system.
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On the incompressible and non-resistive limit of 3D compressible magnetohydrodynamic equations in bounded domains Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-12-05 Xiaoyu Gu, Yaobin Ou
In this paper, we investigate the incompressible and non-resistive limit for the initial boundary value problem of isentropic compressible resistive magnetohydrodynamic equations with ill-prepared initial data in three-dimensional bounded domains. We establish the higher-order uniform estimates with respect to both the Mach number and the resistivity coefficient in the framework of new type of weighted
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Rigidity of three-dimensional steady internal waves with constant vorticity governed by the f-plane approximation Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-12-05 Lili Fan, Ruonan Liu, Qingkun Xiao
This paper investigates the structural implications of constant vorticity for steady three-dimensional internal water waves governed by the equatorial f-plane approximation. Under the assumption that the first components of the non-zero constant vorticity vectors in the upper and lower layers are zeros, it is proved that every three-dimensional traveling internal wave with bounded velocity is either
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On existence, uniqueness and stability of solutions to Cahn–Hilliard/Allen–Cahn systems with cross-kinetic coupling Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-12-02 A. Brunk, H. Egger, T.D. Oyedeji, Y. Yang, B.-X. Xu
A system of phase-field equations with strong-coupling through state and gradient dependent non-diagonal mobility matrices is studied. Existence of weak solutions is established by the Galerkin approximation and a-priori estimates in strong norms. Relative energy estimates are used to derive a general nonlinear stability estimate. As a consequence, a weak–strong uniqueness principle is obtained and
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Regularity for the steady Stokes-type flow of incompressible Newtonian fluids in some generalized function settings Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-12-01 Minh-Phuong Tran, Thanh-Nhan Nguyen, Hong-Nhung Nguyen
A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving p-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper also provides a relatively complete picture of our main results in two regards: problems with nonlinearity is regular with respect to the gradient variable; and asymptotically
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Periodic traveling waves for a diffusive influenza model with treatment and seasonality Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-27 Dong Deng, Hongxun Wei
This paper is concerned with the existence and nonexistence of time-periodic traveling waves for a diffusive influenza model with treatment and seasonality. By using the next generation operator theory, we first get basic reproduction number R0 for the corresponding periodic ODEs. Then, by constructing sub-and super-solutions and using Schauder’s fixed point theorem, we obtain the existence of time-periodic
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On the stochastic engine of contagious diseases in exponentially growing populations Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-27 Torsten Lindström
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth and death rates in comparison to disease parameters like the contact rate and the removal rate ensures that the globally stable endemic equilibrium corresponds to
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A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-20 Gulsemay Yigit, Wakil Sarfaraz, Raquel Barreira, Anotida Madzvamuse
In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion
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Superlinear degradation in a doubly degenerate nutrient taxis system Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-20 Xu Pan
This work is concerned with the doubly degenerate cross-diffusion system with generalized logistic source ut=∇⋅(uv∇u)−∇⋅(u2v∇v)+f(u),x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0in a smoothly bounded domain Ω⊂Rn (n≥2) with no-flux boundary conditions, where f(u)=ρu−μuκ with ρ,μ>0. It is shown that under the assumption that u0∈W1,∞(Ω) is nonnegative with u0⁄≡0 and v0∈W1,∞(Ω) is positive in Ω̄, if κ>(n+2)/2,then the problem
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Asymptotic behaviour of general nonautonomous Nicholson equations with mixed monotonicities Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-21 Teresa Faria
A general nonautonomous Nicholson equation with multiple pairs of delays in mixed monotone nonlinear terms is studied. Sufficient conditions for permanence are given, with explicit lower and upper uniform bounds for all positive solutions. Imposing an additional condition on the size of some of the delays, and by using an adequate difference equation of the form xn+1=h(xn), we show that all positive
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Invasion analysis of a reaction–diffusion-advection predator–prey model in spatially heterogeneous environment Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-23 Yihuan Sun
In this paper, we study a reaction–diffusion–advection predator–prey model with Holling type-II functional response in heterogeneous environment is considered, where the prey are subject to both random and directed movements. We show the effect of changes in diffusion rates of predator and prey on whether prey can be invaded when advection rate is small. Moreover, we show that the predator with a large
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Dynamics of a reaction–diffusion waterborne pathogen model with free boundaries Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-21 Meng Zhao
In this paper, we consider a reaction–diffusion waterborne pathogen model with free boundary. We first prove that this problem has a unique global solution, and then we show that its longtime behavior is determined by a spreading–vanishing dichotomy. Moreover, we obtain sharp criteria for spreading and vanishing, which is very different from the results in Zhou et al. (2018) that the epidemic will
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The Boltzmann equation for plane Couette flow in a finite channel Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-22 Xuan Ma, Yating Wang
The dynamics of a rarefied gas in a finite channel with the same temperatures and opposite velocities is a fundamental problem in kinetic theory. The relative motion of the planar boundaries can induce a non-equilibrium state which is referred to as the Couette flow. In this paper, we demonstrate that the unsteady Couette flow for the Boltzmann equation in 3D finite channel time asymptotically converges
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Phase separation and morphology formation in interacting ternary mixtures under evaporation: Well-posedness and numerical simulation of a non-local evolution system Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-22 Rainey Lyons, Emilio N.M. Cirillo, Adrian Muntean
We study a nonlinear coupled parabolic system with non-local drift terms modeling at the continuum level the inter-species interaction within a ternary mixture that allows the evaporation of one of the species. In the absence of evaporation, the proposed system coincides with the hydrodynamic limit of a stochastic interacting particle system of Blume–Capel-type driven by the Kawasaki dynamics. Similar
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On Lewy Stampacchia inequalities for a pseudomonotone parabolic obstacle problem with L1-data Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-16 Olivier Guibé, Yassine Tahraoui, Guy Vallet
The aim of this paper is to prove the existence of entropy solution, and the associated Lewy-Stampacchia inequalities in a renormalized form, to some parabolic obstacle problems governed by a Leray-Lions pseudomonotone operator in the presence of L1-data and homogeneous Dirichlet boundary conditions.
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Finite-time blow-up and boundedness in a quasilinear attraction–repulsion chemotaxis system with nonlinear signal productions Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-13 Zhan Jiao, Irena Jadlovská, Tongxing Li
This article is focused on the no-flux attraction–repulsion chemotaxis model ut=∇⋅(D(u)∇u−S(u)∇v+T(u)∇w)+h(u),x∈Ω,t>0,0=Δv−α(t)+f(u),x∈Ω,t>0,0=Δw−β(t)+g(u),x∈Ω,t>0defined in a smooth and bounded domain Ω⊂Rn(n≥2) and subjected to homogeneous Neumann boundary conditions. The functions D,S and T suitably generalize the singular prototypes D(s)=(s+1)m1−1,S(s)=s(s+1)m2−1,T(s)=s(s+1)m3−1,s≥0,m1,m2,m3∈R,and
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Analysis of a mathematical model arising from stage-structured predator–prey in a chemostat Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-09 Hui Zhou
In this article, we consider a 4-dimensional predator–prey chemostat model of nitrogen-phytoplankton-rotifer interactions with staged structure proposed by Blasius et al. (2020). Although it is still difficult to prove the simulation observations in Blasius et al. (2020) by mathematical arguments, we explore the dynamics in order to better understand the dynamical mechanism of cyclic persistence for
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Effect models for the stationary Navier–Stokes fluid in a porous medium with different scales Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-10-31 Hongxing Zhao
In this paper, we investigate an incompressible flow through a thin corrugated domain fill with fluid saturated porous medium. The porous medium flow is governed by Navier–Stokes model. The thickness of the domain is assumed to be aɛ and the solid part is supposed to be periodical cylinders of size ɛ. We rigorously derive different asymptotic models by comparing the relation between ɛ and aɛ. To prove
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Global well-posedness for the Euler-alignment system with singular communication weights in multi-dimensions Nonlinear Anal. Real World Appl. (IF 2.0) Pub Date : 2023-11-01 Young-Pil Choi, Jinwook Jung
We study the global-in-time well-posedness for the pressureless Euler-alignment system with singular communication weights ϕ(r)=r−γ, γ∈(0,d). Here d∈N denotes the dimension. Under the assumptions that the initial density has a compact support and the initial velocity is sufficiently small, we construct a global-in-time bounded solution by means of the method of characteristics. The uniqueness is also