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Existence and Localization of Unbounded Solutions for Fully Nonlinear Systems of Jerk Equations on the Half-Line Acta Appl. Math. (IF 1.6) Pub Date : 2024-03-13 Ali Zerki, Kamal Bachouche, Karima Ait-Mahiout
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An Attraction-Repulsion Chemotaxis System: The Roles of Nonlinear Diffusion and Productions Acta Appl. Math. (IF 1.6) Pub Date : 2024-03-13 Zhan Jiao, Irena Jadlovská, Tongxing Li
This article considers the no-flux attraction-repulsion chemotaxis model $$ \left \{ \textstyle\begin{array}{l} \begin{aligned} &u_{t} = \nabla \cdot \big((u+1)^{m_{1}-1}\nabla u-\chi u(u+1)^{m_{2}-2} \nabla v+\xi u(u+1)^{m_{3}-2}\nabla w\big),& x\in \Omega ,\ t>0&, \\ & 0=\Delta v+f(u)-\beta v, & x\in \Omega ,\ t>0&, \\ & 0=\Delta w+g(u)-\delta w, & x\in \Omega ,\ t>0& \end{aligned} \end{array}\displaystyle
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Uniform Turnpike Property and Singular Limits Acta Appl. Math. (IF 1.6) Pub Date : 2024-03-07 Martín Hernández, Enrique Zuazua
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Swarm-Based Optimization with Random Descent Acta Appl. Math. (IF 1.6) Pub Date : 2024-03-01
Abstract We extend our study of the swarm-based gradient descent method for non-convex optimization, (Lu et al., Swarm-based gradient descent method for non-convex optimization, 2022, arXiv:2211.17157), to allow random descent directions. We recall that the swarm-based approach consists of a swarm of agents, each identified with a position, \(\mathbf{x}\) , and mass, \(m\) . The key is the transfer
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Asymptotic Monotonicity of Positive Solutions for Fractional Parabolic Equation on the Right Half Space Acta Appl. Math. (IF 1.6) Pub Date : 2024-02-26 Dongyan Li, Yan Dong
In this paper, we mainly study the asymptotic monotonicity of positive solutions for fractional parabolic equation on the right half space. First, a narrow region principle for antisymmetric functions in unbounded domains is obtained, in which we remarkably weaken the decay condition \(u\rightarrow 0\) at infinity and only assume its growth rate does not exceed \(|x|^{\gamma }\) (\(0 < \gamma < 2s\))
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Differential History-Dependent Variational-Hemivariational Inequality with Application to a Dynamic Contact Problem Acta Appl. Math. (IF 1.6) Pub Date : 2024-02-12 Abderrahmane Oultou, Zakaria Faiz, Othmane Baiz, Hicham Benaissa
This paper is dedicated to the discussion of a new dynamical system involving a history-dependent variational-hemivariational inequality coupled with a non-linear evolution equation. The existence and uniqueness of the solution to this problem are established using the Rothe method and a surjectivity result for a pseudo-monotone perturbation of a maximal operator. Additionally, we derive the regularity
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On Stationary Navier-Stokes Equations in the Upper-Half Plane Acta Appl. Math. (IF 1.6) Pub Date : 2024-02-05 Adrian D. Calderon, Van Le, Tuoc Phan
We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on the external forces. Weak-strong uniqueness criteria based on various growth conditions at the infinity of weak solutions are also given. This is done by employing
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Nonlinear Degenerate Parabolic Equations with a Singular Nonlinearity Acta Appl. Math. (IF 1.6) Pub Date : 2024-01-30 Hichem Khelifi, Fares Mokhtari
In this paper, we study the existence and regularity results for some parabolic equations with degenerate coercivity, and a singular right-hand side. The model problem is $$ \left \{ \textstyle\begin{array}{l@{\quad }l} \frac{\partial u}{\partial t}-\text{div} \left ( \frac{\left (1+\vert \nabla u\vert ^{-\Lambda }\right )\vert \nabla u\vert ^{p-2}\nabla u}{(1+\vert u\vert )^{\theta }} \right )=\f
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A Note on the Discrete Coagulation Equations with Collisional Breakage Acta Appl. Math. (IF 1.6) Pub Date : 2024-01-30 Mashkoor Ali, Ankik Kumar Giri
This article establishes the existence of global classical solutions to discrete coagulation equations with collisional breakage for collision kernels having linear growth. In contrast, the uniqueness is shown under additional restrictions on collision kernels. Moreover, mass conservation property and the positivity of solutions are also shown. While coagulation dominates, the occurrence of the gelation
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Global Existence of Solutions to the Spherically Symmetric Einstein-Vlasov-Maxwell System Acta Appl. Math. (IF 1.6) Pub Date : 2024-01-24
Abstract We prove that the initial value problem with small data for the asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system admits the global in time solution in the case of the non-zero shift vector. This result extends the one already known for chargeless case.
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Mathematical Scrutiny of Singular Predator-Prey Model with Stage-Structure of Prey Acta Appl. Math. (IF 1.6) Pub Date : 2024-01-11 U. Yadav, A. K. Nayak, S. Gakkhar
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Nonuniform Sampling Theorem for Non-decaying Signals in Mixed-Norm Spaces $L_{\vec{p},\frac{1}{\omega }}(\mathbb{R}^{d})$ Acta Appl. Math. (IF 1.6) Pub Date : 2024-01-11 Junjian Zhao
In this paper, combining the non-decaying properties with the mixed-norm properties, the revelent sampling problems are studied under the target space of \(L_{\vec{p},\frac{1}{\omega }}(\mathbb{R}^{d})\). Firstly, we will give a stability theorem for the shift-invariant subspace \(V_{\vec{p},\frac{1}{\omega }}(\varphi )\). Secondly, an ideal sampling in \(W_{\vec{p},\frac{1}{\omega }}^{s}(\mathbb{R}^{d})\)
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Exterior Boundary-Value Poincaré Problem for Elliptic Systems of the Second Order with Two Independent Variables Acta Appl. Math. (IF 1.6) Pub Date : 2023-12-21 F. Criado-Aldeanueva, N. Odishelidze, J. M. Sanchez, M. Khachidze
This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do not always cause the normal solvability of formulated exterior elliptic problems in the sense of Noether. Nevertheless, from the system of differential equations
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Boundary Controllability of a Simplified Stabilized Kuramoto-Sivashinsky System Acta Appl. Math. (IF 1.6) Pub Date : 2023-12-12 Víctor Hernández-Santamaría, Alberto Mercado, Piero Visconti
In this paper, we study the controllability of a nonlinear system of coupled second- and fourth-order parabolic equations. This system can be regarded as a simplification of the well-known stabilized Kuramoto-Sivashinsky system. Using only one control applied on the boundary of the second-order equation, we prove that the local-null controllability of the system holds if the square root of the diffusion
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Symmetry of Positive Solutions for Lane-Emden Systems Involving the Logarithmic Laplacian Acta Appl. Math. (IF 1.6) Pub Date : 2023-12-12 Rong Zhang, Vishvesh Kumar, Michael Ruzhansky
We study the Lane-Emden system involving the logarithmic Laplacian: $$ \textstyle\begin{cases} \ \mathcal{L}_{\Delta }u(x)=v^{p}(x) ,& x\in \mathbb{R}^{n}, \\ \ \mathcal{L}_{\Delta }v(x)=u^{q}(x) ,& x\in \mathbb{R}^{n}, \end{cases} $$ where \(p,q>1\), \(n\geq 2\) and \(\mathcal{L}_{\Delta }\) denotes the logarithmic Laplacian arising as a formal derivative \(\partial _{s}|_{s=0}(-\Delta )^{s}\) of
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Topological Travelling Waves of a Macroscopic Swarmalator Model in Confined Geometries Acta Appl. Math. (IF 1.6) Pub Date : 2023-12-14 P. Degond, A. Diez
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Hilbert-Schmidt Numerical Radius of a Pair of Operators Acta Appl. Math. (IF 1.6) Pub Date : 2023-12-04 Soumia Aici, Abdelkader Frakis, Fuad Kittaneh
We introduce a new norm on \(\mathcal{C}_{2}\times \mathcal{C}_{2}\), where \(\mathcal{C}_{2}\) is the Hilbert-Schmidt class. We study basic properties of this norm and prove inequalities involving it. As an application of the present study, we deduce a chain of new bounds for the Hilbert-Schmidt numerical radii of \(2\times 2\) operator matrices. Connection with the classical Hilbert-Schmidt numerical
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Asymptotic Flocking for the Cucker-Smale Model with Time Variable Time Delays Acta Appl. Math. (IF 1.6) Pub Date : 2023-12-05 Elisa Continelli
In this paper, we investigate a Cucker-Smale flocking model with varying time delay. We establish exponential asymptotic flocking without requiring smallness assumptions on the time delay size and the monotonicity of the influence function.
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A Direct Proof of Linear Decay Rate for Euler-Coriolis Equations Acta Appl. Math. (IF 1.6) Pub Date : 2023-11-28 Siqi Ren
In this paper, we give a direct proof of \(t^{-1}\) (optimal) linear decay rate for Euler-Coriolis equations in \(L^{\infty }\) space-time. Our proof is based on a proper decomposition of the explicit solution and \(L^{\infty }\) estimate for the kernels, which captures the dispersive mechanism.
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Stability for an Interface Transmission Problem of Wave-Plate Equations with Dynamical Boundary Controls Acta Appl. Math. (IF 1.6) Pub Date : 2023-11-22 Zahraa Abdallah, Stéphane Gerbi, Chiraz Kassem, Ali Wehbe
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Incompressible Limits of the Patlak-Keller-Segel Model and Its Stationary State Acta Appl. Math. (IF 1.6) Pub Date : 2023-11-17 Qingyou He, Hai-Liang Li, Benoît Perthame
We complete previous results about the incompressible limit of both the \(n\)-dimensional \((n\geq 3)\) compressible Patlak-Keller-Segel (PKS) model and its stationary state. As in previous works, in this limit, we derive the weak form of a geometric free boundary problem of Hele-Shaw type, also called congested flow. In particular, we are able to take into account the unsaturated zone, and establish
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On Cumulative Tsallis Entropies Acta Appl. Math. (IF 1.6) Pub Date : 2023-11-13 Thomas Simon, Guillaume Dulac
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Stability of a Vector-Borne Disease Model with a Delayed Nonlinear Incidence Acta Appl. Math. (IF 1.6) Pub Date : 2023-11-14 Ali Traoré
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Stability by Polynomial Squeezing for a Class of Energy Damping Plate Models Acta Appl. Math. (IF 1.6) Pub Date : 2023-11-07 Flank D. M. Bezerra, Linfang Liu, Vando Narciso
In this work we consider a semilinear plate equation with non-constant material density in the context of energy damping models. Existence and uniqueness of regular and generalized solutions are established. The energy associated to this equation is shown to posses a compressed polynomial decay range.
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Detached Shock Past a Blunt Body Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-31 Myoungjean Bae, Wei Xiang
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Bistability and Oscillatory Behaviours of Cyclic Feedback Loops Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-31 Jules Guilberteau
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Existence of Signed and Sign-Changing Solutions for Weighted Kirchhoff Problems with Critical Exponential Growth Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-24 Brahim Dridi, Rached Jaidane, Rima Chetouane
This work is devoted to study the existence of least energy sign-changing solutions for a nonlocal weighted Schrödinger-Kirchhoff problem in the unit ball \(B\) of \(\mathbb{R}^{N}\), \(N>2\). The non-linearity of the equation is assumed to have exponential growth in view of Trudinger-Moser type inequalities. In order to obtain our existence result, we use the constrained minimization in Nehari set
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Concentration Phenomena of Riemann Solutions to a Logarithmic Perturbed Model Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-18 Shiwei Li
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Non-Trivial Periodic Solutions for a Class of Second Order Differential Equations with Large Delay Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-17 Adrian Gomez, Nolbert Morales, Manuel Zamora
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Principal and Nonprincipal Solutions of Impulsive Dynamic Equations: Leighton and Wong Type Oscillation Theorems Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-17 A. Zafer, S. Doğru Akgöl
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Periodic $\mathrm{L}_{p}$ Estimates by ℛ-Boundedness: Applications to the Navier-Stokes Equations Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-16 Thomas Eiter, Mads Kyed, Yoshihiro Shibata
General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw’s transference principle, time-periodic \(\mathrm {L}_{p}\) estimates of maximal regularity type are carried over from ℛ-bounds of the family of solution operators (ℛ-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier-Stokes
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Existence Result for Solutions to Some Noncoercive Elliptic Equations Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-13 A. Marah, H. Redwane
In this work, we study a class of degenerate Dirichlet problems, whose prototype is $$ \left \{ \begin{aligned} &-{\mathrm{div}}\Big(\frac{\nabla u}{(1+|u|)^{\gamma }}+c(x)|u|^{\theta -1}u \log ^{\beta }(1+|u|)\Big)= f\ \ {\mathrm{in}}\ \Omega , \\ & u=0\ \ {\mathrm{on}}\ {\partial \Omega }, \end{aligned} \right . $$ where \(\Omega \) is a bounded open subset of \(\mathbb{R}^{N}\). \(0<\gamma <1\)
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Reduced AKNS Spectral Problems and Associated Complex Matrix Integrable Models Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-11 Wen-Xiu Ma
The aim of this paper is to conduct two group reductions for matrix spectral problems simultaneously. We formulate reduced Ablowitz-Kaup-Newell-Segur matrix spectral problems under two local group reductions, and construct associated hierarchies of matrix integrable models, which keep the corresponding zero curvature equations invariant. In this way, various integrable models can be generated via zero
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On the Large Data Global Well-Posedness of Inviscid Axially Symmetric MHD-Boussinesq System Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-03 Zijin Li, Zhaojun Xing, Meixian Yang
The global well-posedness of the 3D inviscid MHD-Boussinesq system, with large axisymmetric initial data, in the Sobolev space \(H^{m}\) is given. To overcome difficulties that arise in the time-uniform \(H^{1}\) estimate, a reformulated system of good unknowns is discovered and an intermediate estimate is shown. Based on the reformulated system, a Beale-Kato-Majda-type criterion of the inviscid MHD-Boussinesq
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Exponential Stability for a Bresse System with Hybrid Dissipation Acta Appl. Math. (IF 1.6) Pub Date : 2023-10-03 Rawlilson O. Araújo
A new Bresse system with hybrid damping coming from elasticity, thermoelasticity, and viscoelasticity, is analyzed. The uniform (exponential) stabilization of semigroup solution is proved under the dynamic response of each hybrid damping effect.
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Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach Acta Appl. Math. (IF 1.6) Pub Date : 2023-09-29 Blaise Colle, Jérôme Lohéac, Takéo Takahashi
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Dispersive Effects in Two- and Three-Dimensional Peridynamics Acta Appl. Math. (IF 1.6) Pub Date : 2023-09-29 A. Coclite, G. M. Coclite, G. Fanizza, F. Maddalena
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New Type of Fractal Functions for the General Data Sets Acta Appl. Math. (IF 1.6) Pub Date : 2023-09-25 Manuj Verma, Amit Priyadarshi
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A Refinement of the First Eigenvalue and Eigenfunction of the Linearized Moser-Trudinger Problem Acta Appl. Math. (IF 1.6) Pub Date : 2023-09-20 Kefan Pan, Jing Yang
We revisit the following Moser-Trudinger problem $$ \textstyle\begin{cases} -\Delta u=\lambda ue^{u^{2}} &\text{in } \Omega , \\ u>0&\text{in } \Omega , \\ u=0 &\text{on } \partial \Omega , \end{cases} $$ where \(\Omega \subset \mathbb{R}^{2}\) is a smooth bounded domain and \(\lambda >0\) is sufficiently small. Qualitative analysis of peaked solutions for Moser-Trudinger type equation in \(\mathbb{R}^{2}\)
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Stabilization Effects of Magnetic Field on a 2D Anisotropic MHD System with Partial Dissipation Acta Appl. Math. (IF 1.6) Pub Date : 2023-09-11 Dongxiang Chen, Fangfang Jian
To uncover that the magnetic field mechanism can stabilize electrically conducting turbulent fluids, we investigate the stability of a special two dimensional anisotropic MHD system with vertical dissipation in the horizontal velocity component and partial magnetic damping near a background magnetic field. Since the MHD system has only vertical dissipation in the horizontal velocity and vertical magnetic
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On the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order Terms Acta Appl. Math. (IF 1.6) Pub Date : 2023-09-13 Marco Discacciati, Claudia Garetto, Costas Loizou
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Symmetries and Exact Solutions of the Diffusive Holling–Tanner Prey-Predator Model Acta Appl. Math. (IF 1.6) Pub Date : 2023-09-06 Roman Cherniha, Vasyl’ Davydovych
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Global Bounded Solution in a Chemotaxis-Stokes Model with Porous Medium Diffusion and Singular Sensitivity Acta Appl. Math. (IF 1.6) Pub Date : 2023-09-04 Jianping Wang
This article is concerned with a chemotaxis-Stokes system with porous medium diffusion and singular sensitivity: $$\begin{aligned} \left \{ \textstyle\begin{array}{l@{\quad }l} n_{t}+u\cdot \nabla n=\nabla \cdot (D(n)\nabla n)-\nabla \cdot (nS(x,n,c)\cdot \nabla c),&x\in \Omega ,\ \ t>0, \\ c_{t}+u\cdot \nabla c=\Delta c-nc,&x\in \Omega ,\ \ t>0, \\ u_{t}+\nabla P=\Delta u+n\nabla \Phi ,\ \ \ \nabla
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Vanishing Micro-Rotation and Angular Viscosities Limit for the 2D Micropolar Equations in a Bounded Domain Acta Appl. Math. (IF 1.6) Pub Date : 2023-08-30 Yangyang Chu, Yuelong Xiao
In this paper, we investigate the vanishing micro-rotation and angular viscosities limit of solutions to the 2D incompressible micropolar equations in a bounded domain with Navier-type boundary conditions satisfied by the velocity field. In a general bounded smooth domain \(\Omega \), we establish the uniform \(H^{2}(\Omega )\) estimates (independent of the micro-rotation and angular viscosities) of
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Exponential Ergodicity of a Degenerate Age-Size Piecewise Deterministic Process Acta Appl. Math. (IF 1.6) Pub Date : 2023-08-30 Ignacio Madrid
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On the Homogenization of the Renewal Equation with Heterogeneous External Constraints Acta Appl. Math. (IF 1.6) Pub Date : 2023-08-30 Étienne Bernard, Francesco Salvarani
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Frictionless Signorini’s Contact Problem for Hyperelastic Materials with Interior Point Optimizer Acta Appl. Math. (IF 1.6) Pub Date : 2023-08-29 Houssam Houssein, Simon Garnotel, Frédéric Hecht
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Two-Flow Instability of One Class of Spherically Symmetric Dynamic Equilibrium States of Vlasov-Poisson Plasma Acta Appl. Math. (IF 1.6) Pub Date : 2023-08-24 S. A. Bibilova, Y. G. Gubarev
The problem on linear stability of particular class of spherically symmetric states of dynamic equilibrium of the Vlasov-Poisson plasma, which contains electrons and a single species of ions, is considered. An absolute instability of these equilibrium states with respect to small spherically symmetric perturbations is proved by the direct Lyapunov method in the case when stationary distribution functions
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Dynamical Behavior of a Spatiotemporal Model in Open Advective Environments Acta Appl. Math. (IF 1.6) Pub Date : 2023-08-24 Ying Yu, Zhi Ling, You Zhou
We investigate a reaction-diffusion-advection system describing the interaction between a population and a toxicant in open advective environments. The interesting feature of this model is the consideration of a more general advective term and boundary condition. By applying the theory of monotone semi-flow and principal eigenvalue, we obtain the existence and stability of steady states and further
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Turbulence Phenomena in Magnetohydrodynamic Phase Transitions Acta Appl. Math. (IF 1.6) Pub Date : 2023-08-03 Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
The model developed in (Fabrizio in J. Eng. Math., 2023) and (Fabrizio in Int. J. Eng. Sci. 44:529–539, 2006), involving the use of a local Reynolds number, is applied to describe phase transitions in a fluid. Specifically, it is applied in a magnetohydrodynamics context to study the evolution of turbulence in certain phenomena. The relevant equations describing the system are those of Navier-Stokes
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Finite-Time Blow-up in a Two-Species Chemotaxis-Competition Model with Degenerate Diffusion Acta Appl. Math. (IF 1.6) Pub Date : 2023-08-01 Yuya Tanaka
This paper is concerned with the two-species chemotaxis-competition model with degenerate diffusion, $$ \textstyle\begin{cases} u_{t} = \Delta u^{m_{1}} - \chi _{1} \nabla \cdot (u\nabla w) + \mu _{1} u (1-u-a_{1}v), &x\in \Omega ,\ t>0, \\ v_{t} = \Delta v^{m_{2}} - \chi _{2} \nabla \cdot (v\nabla w) + \mu _{2} v (1-a_{2}u-v), &x\in \Omega ,\ t>0, \\ 0 = \Delta w +u+v-\overline{M}(t), &x\in \Omega
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Global Stability of a Conduction-Diffusion System with Superimposed Plane Parallel Shear Flows Acta Appl. Math. (IF 1.6) Pub Date : 2023-07-21 Lanxi Xu, Haijia Xu
Nonlinear stability of plane parallel convective shear flows of a binary fluid mixture heated and salted from below is investigated by generalized energy method. Through defining a new energy functional, a sufficient condition for unconditional nonlinear exponential stability of the basic motions is proved in the case of streamwise perturbation. The results in the paper have improved the results in
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Weighted Pseudo Almost Periodic Synchronization for Clifford-Valued Neural Networks with Leakage Delay and Proportional Delay Acta Appl. Math. (IF 1.6) Pub Date : 2023-07-05 Jin Gao, Xiaoli Huang, Lihua Dai
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Z-Eigenvalue Localization Sets for Tensors and the Applications in Rank-One Approximation and Quantum Entanglement Acta Appl. Math. (IF 1.6) Pub Date : 2023-07-05 Juan Zhang, Xuechan Chen
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Upper Semicontinuity of Pullback Attractors for Nonlinear Full Von Kármán Beam Acta Appl. Math. (IF 1.6) Pub Date : 2023-07-03 Moncef Aouadi, Souad Guerine
In this paper we study the long-time dynamics of pullback attractors for non-autonomous and nonlinear full von Kármán beam and its upper-semicontinuity property. The one-dimensional full von Kármán beam equations constitutes a basic model to describe the nonlinear oscillations with large displacements due the existence of nonlinear terms in the motion equations. Under quite general assumptions on nonlinear
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Rapid Stabilization of Timoshenko Beam System with the Internal Delay Control Acta Appl. Math. (IF 1.6) Pub Date : 2023-07-03 Yaru Xie, Yuwen Chen
In this paper, we are concerned with rapid stabilization of Timoshenko beam system with the internal delay control. The main idea of solving the stabilization problem is transformation. The original time delay system is firstly transformed into the undelayed system, and then the feedback control law which can stabilize the undelayed system is found. Finally, we prove that the feedback control law can
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A Case Study of Separability of Second-Order Differential Equations Acta Appl. Math. (IF 1.6) Pub Date : 2023-07-03 Willy Sarlet
We perform a systematic study and classification of the possibility to decouple a class of second-order differential equations which have quadratic terms, either in the velocities or in the coordinates, plus linear damping terms. Our basic approach is the existing coordinate-free theory for the characterization of separable systems. But the focus on this specific class of second-order equations spontaneously
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Local Existence and Uniqueness of Strong Solution to the Inhomogeneous Primitive Equations with Vacuum Acta Appl. Math. (IF 1.6) Pub Date : 2023-06-27 Xiaoling Hu, Kunzhuo Tong, Xiaojing Xu
In this paper, we establish the existence and uniqueness of the local strong solution to the Cauchy problem of the inhomogeneous incompressible primitive equations in a periodic domain. Inspired by the work (J. Li in J. Differ. Equ. 263:6512–6536, 2017), we remove the compatibility condition required in (Q. Jiu and F. Wang in Acta Math. Sci. Ser. B Engl. Ed. 40:1316–1334, 2020), and permit the initial
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Normalized Ground States for the Mass-Energy Doubly Critical Kirchhoff Equations Acta Appl. Math. (IF 1.6) Pub Date : 2023-06-27 Lingzheng Kong, Haibo Chen
In this paper, we study the normalized solutions for the nonlinear critical Kirchhoff equations with combined nonlinearities in \(\mathbb{R}^{4}\). In particular, in the case of \(N=4\), there is a new mass-energy doubly critical phenomenon for Kirchhoff equation with combined nonlinearities that the mass critical exponent \(2+\frac{8}{N}\) is equal to the energy critical exponent \(\frac{2N}{N-2}\)
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Decay Rates for Mild Solutions of the Quasi-Geostrophic Equation with Critical Fractional Dissipation in Sobolev-Gevrey Spaces Acta Appl. Math. (IF 1.6) Pub Date : 2023-06-20 Wilberclay G. Melo, Natã Firmino Rocha, Natielle dos Santos Costa
We study the existence of mild solutions for the Quasi-geostrophic equation with critical fractional dissipation in Sobolev-Gevrey spaces. In order to be more specific, by assuming that the initial data \(\theta _{0}\in \dot{H}_{a,\sigma }^{s}(\mathbb{R}^{2})\) (with \(a>0\), \(\sigma > 1\), \(s\in [0,1)\)) is small enough, we prove that there is a unique global in time (mild) solution $$ \theta \in