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A monotone block coordinate descent method for solving absolute value equations Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-30 Tingting Luo, Jiayu Liu, Cairong Chen, Qun Wang
In Noor et al. (2011), the second-order Taylor expansion of the objective function is incorrectly used in constructing the descent direction. Thus, the proposed block coordinate descent method is non-monotone and a strict convergence analysis is lack. This motivates us to propose a monotone block coordinate descent method for solving absolute value equations. Under appropriate conditions, we analyze
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Analysis of an HIV latent infection model with cell-to-cell transmission and multiple drug classes Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-29 Yaqin Huang, Xin Meng, Xia Wang, Libin Rong
In this paper, we investigate an HIV latent infection model that incorporates cell-to-cell transmission and multiple drug classes, extending the model proposed by Areej Alshorman et al. (2022). We derive the basic reproduction number R0 for the model and establish the existence and local stability of its equilibria. By constructing appropriate Lyapunov functions, we analyze the global stability of
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Finite element method for the coupled Stokes–Darcy–Darcy system Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-29 Liyun Zuo, Guangzhi Du
In this article, we propose and analyze the finite element method for the mixed Stokes–Darcy–Darcy system which involves free flow in conduits coupled with confined flow in fractured porous media. The interactions on the interfaces come from the classical Stokes–Darcy system and the famous bulk-fracture system. Rigorously theoretical results are derived and some numerical results are provided to verify
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High-order Runge–Kutta type large time-stepping schemes for the compressible Euler equations Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-27 Lele Liu, Songhe Song
This paper establishes a class of up to fourth-order large time-stepping schemes for the compressible Euler equations under the stabilization technique framework. The proposed schemes do not destroy the accuracy of the underlying strong-stability-preserving Runge–Kutta (SSPRK) schemes, and their time step is at most s times that of the forward Euler time step of the underlying s-stage, pth-order SSPRK
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Real solutions to an asymptotically linear Helmholtz equation Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-27 Biao Liu, Ruowen Qiu, Fukun Zhao
In this paper, we study real solutions of the nonlinear Helmholtz equation −Δu−k2u=f(x,u),x∈RN, satisfying the asymptotic conditions u(x)=O|x|1−N2and∂2u∂r2(x)+k2u(x)=o|x|1−N2asr=|x|→∞.
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Threshold behavior of a stochastic predator–prey model with fear effect and regime-switching Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-26 Jing Ge, Weiming Ji, Meng Liu
This work proposes a stochastic predator–prey model with fear effect and regime-switching. It is testified that the dynamical behaviors of the model are determined by two thresholds F1 and G: if both F1 and G are positive, then the model admits a unique stationary distribution with the ergodic property; if F1 is positive and G is negative, then the predator population dies out and the prey population
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Positive recurrence of a stochastic heroin epidemic model with standard incidence and telegraph noise Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-25 Yu Chen, Xiaofeng Zhang
The heroin epidemic has posed a serious threat to public health and social stability. Understanding the dynamics of the heroin epidemic model is of great significance for formulating effective prevention and control strategies. In this paper, a stochastic heroin epidemic model with standard incidence and telegraph noise is considered. By constructing a suitable stochastic Lyapunov function with regime
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An effective operator splitting scheme for general motion by mean curvature using a modified Allen–Cahn equation Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-24 Zihan Cao, Zhifeng Weng, Shuying Zhai
We present a fast and effective method for modeling general motion by mean curvature based on a modified Allen–Cahn equation. Employing the second-order operator time-splitting method, the original problem is discretized into three subproblems based on the different natures of each part of the model: the heat equation is solved by a Crank–Nicolson (CN) alternating direction implicit (ADI) finite difference
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Improvement of conditions for global solvability in a chemotaxis system with signal-dependent motility and generalized logistic source Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-23 Changfeng Liu, Jianping Gao
This paper deals with a chemotaxis system with signal-dependent motility ut=∇⋅(γ(v)∇u)−∇⋅(χ(v)u∇v)+λu−μulx∈Ω,t>0,vt=Δv−v+ux∈Ω,t>0,∂νu=∂νv=0x∈∂Ω,t>0,u(x,0)=u0(x)≥0,v(x,0)=v0(x)≥0x∈Ω, under homogeneous Neumann boundary conditions in a bounded domain Ω⊂Rn(n>2). If λ∈R and μ>0 are constants, we prove that this problem possesses a global classical solution that is uniformly bounded under the conditions
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Novel Razumikhin-type finite-time stability criteria of fractional nonlinear systems with time-varying delay Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-23 Shuihong Xiao, Jianli Li
This paper investigates the finite-time stability (FTS) of fractional-order nonlinear systems with time-varying delay (FONDSs). Unlike most of the existing literatures on FTS of fractional-order nonlinear delayed systems by means of establishing delayed integral inequalities, several Razumikhin-type Lyapunov conditions are presented in this paper. Using these results, we derive stability criteria for
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Dispersive shock waves in the fifth-order modified KdV equation Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-22 Dong-Rao Jing, Hai-Qiang Zhang, Nan-Nan Wei
This study focuses on the Whitham modulation theory of the fifth-order modified KdV equation (5mKdV), successfully deriving the solutions for modulated periodic waves and establishing corresponding Whitham equations. Through the detailed analysis of the initial step solution, the rarefaction waves and two types of dispersive shock wave structures are revealed. Our results not only enrich the theoretical
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Localized Hermite method of approximate particular solutions for solving the Poisson equation Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-21 Kwesi Acheampong, Huiqing Zhu
In this paper, we propose a localized Hermite method of approximate particular solutions (LHMAPS) for solving the Poisson equation. Unlike the localized method of approximate particular solutions (LMAPS) that approximates only function values of the solution in different local neighborhoods of collocation nodes by using particular solutions of radial basis functions, the proposed method employs mixed
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A class of higher-order time-splitting Monte Carlo method for fractional Allen–Cahn equation Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-21 Huifang Yuan, Zhiyuan Hui
In this paper, we introduce a novel class of higher-order time-splitting Monte Carlo method tailored for both fractional and classical Allen–Cahn equations. The proposed method integrates the spectral Monte Carlo method (SMC) with a time-splitting scheme, alternating between efficiently computing the linear propagator via the spectral Monte Carlo method and explicitly evaluating the nonlinear propagator
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On the oscillation of second-order functional differential equations with a delayed damping term Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-17 Osama Moaaz, Higinio Ramos
In this work, we derive some criteria for studying the asymptotic and oscillatory behavior of solutions of functional differential equations with a delayed damping term. Our results extend and improve upon the limited prior research on this type of equations. The primary goal is to derive criteria applicable to both ordinary and non-damped cases, while accounting for the effects of delay functions
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On the relation between the exponential of real matrices and that of dual matrices Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-16 Chengdong Liu, Yimin Wei, Pengpeng Xie
Dual number matrices play a significant role in engineering applications such as kinematics and dynamics. The matrix exponential is ubiquitous in screw-based kinematics. In this paper, we develop an explicit formula for the dual matrix exponential. The result is closely related to the Fréchet derivative, which can be formed by the standard part and dual part of the original matrix. We only need to
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Leighton–Wintner-type oscillation theorem for the discrete [formula omitted]-Laplacian Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-16 Kōdai Fujimoto, Kazuki Ishibashi, Masakazu Onitsuka
This paper addresses oscillation problems for difference equations with a discrete p(k)-Laplacian. In general, applying the Riccati technique to discrete oscillations is difficult. However, this study established a Leighton–Wintner-type oscillation theorem using the Riccati technique. Three examples are provided to illustrate the results. In particular, we examined the oscillatory problem for a certain
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Geometric programming for multilinear systems with nonsingular [formula omitted]-tensors Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-15 Haibin Chen, Guanglu Zhou, Hong Yan
We consider multilinear systems which arise in various applications, such as data mining and numerical differential equations. In this paper, we show that the multilinear system with a nonsingular M-tensor can be formulated equivalently into a geometric programming (GP) problem which can be solved by the barrier-based interior point method with a worst-case polynomial-time complexity. To the best of
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Optimal decay rate to the contact discontinuity for Navier–Stokes equations under generic perturbations Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-14 Lingjun Liu, Guiqin Qiu, Shu Wang, Lingda Xu
This paper investigates the large-time asymptotic behavior of contact waves in 1-D compressible Navier–Stokes equations. We derive the optimal decay rate for generic initial perturbations, meaning the perturbation’s integral does not need to be zero. It is well-known that generic perturbations in Navier–Stokes equations generate diffusion waves, implying that the optimal decay rate for contact waves
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Stability analysis of a conservative reaction–diffusion system with rate controls Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-14 Jie Ding, Fei Xu, Zhi Ling
This paper demonstrates the fundamental properties of a conservative reaction–diffusion system. The solution of the system exists globally and is unique, as well as uniformly converges to its constant equilibrium as time tends to infinity. In addition, the steady-state system only has a constant solution under a mass conservation condition.
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Energy-equidistributed moving mesh strategies for simulating Hamiltonian partial differential equations Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-13 Qinjiao Gao, Zhengjie Sun, Zongmin Wu
This paper presents an innovative energy-equidistributed moving mesh strategy for simulating Hamiltonian partial differential equations (PDEs) characterized by solitons and rapid temporal variations. A novel framework, named the Energy Equidistribution Principles (EEPs), is introduced, highlighting the critical role of energy conservation in achieving accurate simulations. Building on EEPs, three kinds
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[formula omitted] estimates for fully nonlinear parabolic inequalities on [formula omitted] domains Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-13 Xuemei Li
In this paper, we study boundary W2,δ estimates for solution sets of fully nonlinear parabolic inequalities ut−M+(D2u,λ,Λ)≤f(x,t)≤ut−M−(D2u,λ,Λ) on C1,α domains, which generalize results for elliptic equations in Li and Li (2023).
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A novel time-domain SCT-BEM for transient heat conduction analysis Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-11 Xiaotong Gao, Yan Gu, Bo Yu
Accurate and efficient treatment of domain integrals is critical for obtaining reliable and precise boundary element method (BEM) solutions in dynamic or time-dependent problems. Despite the success of existing techniques for handling domain integrals, significant challenges still remain, especially in time-dependent BEM analyses where time-dependent fundamental solutions often result in integrands
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Propagation direction of traveling waves for a class of nonlocal dispersal bistable epidemic models Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-11 Yu-Xia Hao, Guo-Bao Zhang
This work is devoted to studying the propagation direction of the following nonlocal dispersal epidemic model (0.1)∂u∂t=d1∫RJ(y−x)u(y,t)dy−u−u+αv,x∈R,t>0,∂v∂t=d2∫RJ(y−x)v(y,t)dy−v−βv+g(u),x∈R,t>0,where d1,d2,α,β>0. By discussing the case c=0 and using the monotone dependence of the wave speed of traveling wave solutions on parameters, we state the sufficient conditions for the speed c>0 and c<0 under
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A shape-parameterized RBF-partition of unity technique for PDEs Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-10 Roberto Cavoretto, Alessandra De Rossi, Adeeba Haider
In this paper, we study a direct discretization technique based on a radial basis function partition of unity (RBF-PU) method, which is built to numerically solve partial differential equations (PDEs). Unlike commonly used shape parameter free polyharmonic spline kernels, in this work we focus on local radial kernels depending on the shape parameter associated with the basis functions. The resulting
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Darboux transformations and exact solutions of nonlocal Kaup–Newell equations with variable coefficients Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-09 Chen Wang, Yue Shi, Weiao Yang, Xiangpeng Xin
This paper investigates an integrable nonlocal Kaup–Newell (NKN) equation with variable coefficients. Utilizing Lax pair theory, the construction of the variable coefficient NKN equation is presented for the first time, alongside a systematic analysis employing the Darboux transform technique. This approach explicitly derives the form of the nth-order Darboux transform, which is presented for the first
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Elliptic Neumann problems with highly discontinuous nonlinearities Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-07 Giuseppina D’Aguì, Valeria Morabito, Patrick Winkert
This paper investigates nonlinear differential problems involving the p-Laplace operator and subject to Neumann boundary value conditions whereby the right-hand side consists of a nonlinearity which is highly discontinuous. Using variational methods suitable for nonsmooth functionals, we prove the existence of at least two nontrivial weak solutions of such problems.
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Higher-order freak waves of the AB system revisited via a variable separation method Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-07 Minjie Dong, Xiubin Wang
In this work, we theoretically calculate higher-order freak wave solutions of the AB system through a Darboux transformation by a separation of variable method. Furthermore, the dynamics of first-order and second-order freak wave solutions are discussed with some illustrative graphics. In particular, we observe the emergence of a four peaky-shaped freak wave in the second component, which contrasts
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Limit solutions of loop solitons for a compound WKI-SP equation Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-06 Gaizhu Qu, Junyang Zhang, Xiaorui Hu, Shoufeng Shen
We characterize the limit solutions of loop solitons for an integrable compound equation which is a mix of the Wadati-Konno-Ichikawa (WKI) equation and the short-pulse (SP) equation. We do so by taking an ingenious limit on the τ-function derived from Hirota’s bilinear equations of the mKdV-SG (modified Korteweg–de Vries and sine-Gordon) equation. By virtue of a hodograph transformation, we compute
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Exponential stability of a diffusive Nicholson’s blowflies equation accompanying multiple time-varying delays Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-04 Chuangxia Huang, Bingwen Liu
In this paper, we explore a modified diffusive Nicholson’s blowflies equation accompanying multiple pairs of time-varying delays which include distinct diapause and maturation effects. With the help of some differential inequality analyses, we obtain a criterion to assure the stability and exponential attraction of the addressed reaction–diffusion equation accompanying Neumann boundary conditions,
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Energy of steady periodic equatorial water waves in two-layer flows Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-04 Xun Wang, Sanling Yuan, Jin Zhao
In this paper, we present the Euler equation of steady periodic equatorial water waves in two-layer flows with different densities and generalise the two Stokes’ definitions for the velocity of the wave propagation. We further demonstrate that the excess potential energy density of nonlinear equatorial two-layer waves is always positive, while the excess kinetic energy density is negative.
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On a Camassa–Holm type equation describing the dynamics of viscous fluid conduits Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-04 Rafael Granero-Belinchón
In this note we derive a new nonlocal and nonlinear dispersive equations capturing the main dynamics of a circular interface separating a light, viscous fluid rising buoyantly through a heavy, more viscous, miscible fluid at small Reynolds numbers. This equation that we termed the g−model shares some common structure with the Camassa–Holm equation but has additional nonlocal effects. For this new PDE
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Uniqueness of solution for incompressible inhomogeneous Navier–Stokes equations in dimension two Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-03 Yelei Guo, Chinyin Qian
The global existence of solution for 2D inhomogeneous incompressible Navier–Stokes equations is established by Abidi et al. (2024), and the uniqueness of solution is also investigated under some additional conditions on initial density. The purpose of this paper is to obtain the uniqueness of the solution without any additional assumptions on the initial density in case of 2≤p<4. The key strategy is
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A strong mass conservative finite element method for the Navier–Stokes/Darcy coupled system Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-03 Jessika Camaño, Ricardo Oyarzúa, Miguel Serón, Manuel Solano
We revisit the continuous formulation introduced in Discacciati and Oyarzúa (2017) for the stationary Navier–Stokes/Darcy (NSD) coupled system and propose an equivalent scheme that does not require a Lagrange multiplier to enforce the continuity of normal velocities at the interface. Building on this formulation and following a similar approach to Kanschat and Rivière (2010), we derive a mass-conservative
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A free-parameter alternating triangular splitting iteration method for time-harmonic parabolic problems Appl. Math. Lett. (IF 2.9) Pub Date : 2025-01-01 Chengliang Li, Jiashang Zhu, Changfeng Ma
Based on the triangular splitting technique, we introduce a free-parameter alternating triangular splitting (FPATS) method for solving block two-by-two linear systems with applications to time-harmonic parabolic models. In addition, we demonstrate that the FPATS method is unconditionally convergent and outperforms other methods. Numerical results are provided to show the practicality and efficiency
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Time periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-30 Jiayu Deng, Jianhua Liu, Shuguan Ji
This paper is concerned with the existence of periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings. The main contribution of this research lies in the fact that the coupled terms are nonlinear. For the periods having the form T=2π2a−1b (a,b are positive integers), by applying the dual variational method, we establish the existence of the time periodic solution
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Stability of 2D inviscid MHD equations with only fractional magnetic diffusion in the horizontal direction Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-27 Yueyuan Zhong
This paper focuses on a special 2D magnetohydrodynamic (MHD) system with no viscosity and only fractional magnetic diffusion in the horizontal direction on the domain Ω=T×R and T=[0,1] be a periodic box. Due to the lack of the velocity dissipation, this stability problem is not trivial. Without the presence of a magnetic field, the fluid velocity is governed by the 2D incompressible Euler equation
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Local-in-space blow-up of a weakly dissipative generalized Dullin–Gottwald–Holm equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-26 Wenguang Cheng, Bingqi Li
This paper addresses the problems of blow-up for a weakly dissipative generalized Dullin–Gottwald–Holm equation. A new sufficient condition on the initial data is provided to ensure the finite time local-in-space blow-up of strong solutions, which improves the local-in-space blow-up result of Novruzov and Yazar [1].
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Explicit solutions of Genz test integrals Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-26 Vesa Kaarnioja
A collection of test integrals introduced by Genz (1984) has remained popular to this day for assessing the robustness of high-dimensional numerical integration algorithms. However, the explicit solutions to these integrals do not appear to be readily available in the existing literature: typically the true values of the test integrals are simply approximated using “overkill” numerical solutions. In
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Dynamics of a weak-kernel distributed memory-based diffusion model with nonlocal delay effect Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-26 Quanli Ji, Ranchao Wu, Federico Frascoli, Zhenzhen Chen
In this paper, we study a temporally distributed memory-based diffusion model with a weak kernel and nonlocal delay effect. Without diffusion, we present results on the stability and Hopf bifurcation of the positive constant steady state. With the inclusion of diffusion, further results on the stability and steady state bifurcation are derived. Finally, these findings are applied to a population model
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Finite time blow-up for a heat equation in [formula omitted] Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-26 Kaiqiang Zhang
We consider the semilinear heat equation ut−Δu=|u|p−1u+λu,onRnwhere p>1, and λ∈R is a parameter. When λ=0, the equation reduces to the classical heat equation. We reveal that the parameter λ in the linear term plays an important role in the blow-up conditions. Although the solution may blow up in finite time due to the cumulative effect of the nonlinearities, interestingly, we find that for λ>n2, all
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Constructing solutions of the ‘bad’ Jaulent–Miodek equation based on a relationship with the Burgers equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-26 Jing-Jing Su, Yu-Long He, Bo Ruan
The ‘bad’ Jaulent–Miodek (JM) equation describes the wave evolution of inviscid shallow water over a flat bottom in the presence of shear, which is ill-posed and unstable so that its general initial problem on the zero plane is difficult to solve through traditional mesh-based numerical methods. In this paper, using the Darboux transformation, we find a relation between the ‘bad’ JM equation and the
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A second-order accurate numerical method with unconditional energy stability for the Lifshitz–Petrich equation on curved surfaces Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-24 Xiaochuan Hu, Qing Xia, Binhu Xia, Yibao Li
In this paper, we introduce an efficient numerical algorithm for solving the Lifshitz–Petrich equation on closed surfaces. The algorithm involves discretizing the surface with a triangular mesh, allowing for an explicit definition of the Laplace–Beltrami operator based on the neighborhood information of the mesh elements. To achieve second-order temporal accuracy, the backward differentiation formula
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Uniqueness of identifying multiple parameters in a time-fractional Cattaneo equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-21 Yun Zhang, Xiaoli Feng
This paper addresses an inverse problem involving the simultaneous identification of the fractional order, potential coefficient, initial value and source term in a time-fractional Cattaneo equation. Utilizing the method of Laplace transformation, we demonstrate that the multiple unknowns can be uniquely determined from observational data collected at two boundary points.
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An unstructured algorithm for the singular value decomposition of biquaternion matrices Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-21 Gang Wang
With the modeling of the biquaternion algebra in multidimensional signal processing, it has become possible to address issues such as data separation, denoising, and anomaly detection. This paper investigates the singular value decomposition of biquaternion matrices (SVDBQ), establishing an SVDBQ theorem that ensures unitary matrices formed by the left and right singular vectors, while also introducing
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On trapped lee waves with centripetal forces Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-20 Tao Li, JinRong Wang
This paper firstly studies exact solutions to the atmospheric equations of motion in the f-plane and β-plane approximations while considering centripetal forces. The obtained solutions are shown in Lagrangian coordinates. Additionally, we derive the dispersion relations and perform a qualitative analysis of density, pressure, and vorticity.
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Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-19 Haoyuan Gong, Tongtong Zhou, Baochang Shi, Rui Du
The surface quasi-geostrophic equations with fractional Laplacian are important in the field of oceanic and atmospheric dynamics. In this paper, a new lattice Boltzmann model is proposed to solve the equations. We first obtain an approximation of the governing equation based on the Fourier transform and Gaussian quadrature formula. An LBGK model with a suitable equilibrium distribution function is
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Lyapunov functions for some epidemic model with high risk and vaccinated class Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-19 Ran Zhang, Xue Ren
This paper considers the global asymptotic stability of a model with epidemic model with high risk and vaccinated class, and extends the related methods to two case of reaction–diffusion equations. The results presented here generalize those from Movahedi (2024).
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Stability and Turing bifurcation in a non-local reaction–diffusion equation with a top-hat kernel Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-19 Ying Li, Yongli Song
In the non-local reaction–diffusion equation, the form of the kernel function has an important effect on the dynamics of the equation. In this paper, we study the spatiotemporal dynamics of a class of non-local reaction–diffusion equation where the non-locality is described by the top-hat function with the perceptual radius. The perceptual radius establishes a bridge between the local equation and
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A new structure-preserving method for dual quaternion Hermitian eigenvalue problems Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-18 Wenxv Ding, Ying Li, Musheng Wei
Dual quaternion matrix decompositions have played a crucial role in fields such as formation control and image processing in recent years. In this paper, we present an eigenvalue decomposition algorithm for dual quaternion Hermitian matrices. The proposed algorithm is founded on the structure-preserving tridiagonalization of the dual matrix representation of dual quaternion Hermitian matrices through
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Infinitely many positive periodic solutions for second order functional differential equations Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-18 Weibing Wang, Shen Luo
In this paper, we study the existence of infinitely many positive periodic solutions to a class of second order functional differential equations which cannot be applied directly to the fixed point theorem in cone. With suitable deformations, we construct the operator whose fixed point is closely related to the periodic solution of the original equation and show that the problem has infinitely many
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Normalized solutions to HLS lower critical Choquard equation with inverse-power potential and square-root-type nonlinearity Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-18 Jianlun Liu, Hong-Rui Sun, Ziheng Zhang
This paper is concerned with the HLS lower critical Choquard equation with inverse-power potential and square-root-type nonlinearity. After giving a novel proof of subadditivity of the constraint minimizing problem and establishing the Brézis–Lieb lemma for square-root-type nonlinearity, we not only prove the existence of normalized solutions but also give its energy estimate.
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Global attractor for an age-structured HIV model with nonlinear incidence rate Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-18 Ru Meng, Tingting Zheng, Yantao Luo, Zhidong Teng
Using the method of characteristics and defining one auxiliary function, we prove the existence of global attractor for a general age-structured HIV model, which can be used to solve the uniformly persistence problem in the Kumar and Abbas (2022).
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On a new mechanism of the emergence of spatial distributions in biological models Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-17 B. Kazmierczak, V. Volpert
Non-uniform distributions of various biological factors can be essential for tissue growth control, morphogenesis or tumor growth. The first model describing the emergence of such distributions was suggested by A. Turing for the explanation of cell differentiation in a growing embryo. In this model, diffusion-driven instability of the homogeneous in space solution appears due to the interaction of
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Infinitely many sign-changing normalized solutions for nonlinear scalar field equations Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-15 Jiaxin Zhan, Jianjun Zhang, Xuexiu Zhong, Jinfang Zhou
We study the existence of infinitely many sign-changing solutions to the following nonlinear scalar Schrödinger equation −Δu+λu=f(u)inRNwith a prescribed mass ∫RN|u|2dx=a. Here f∈C1(R,R), a>0 is a given constant and λ∈R is an unknown parameter appearing as a Lagrange multiplier. Jeanjean and Lu have established the existence of infinitely many sign-changing normalized solutions in [Nonlinearity 32
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Spatiotemporal dynamics in a three-component predator–prey model Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-14 Mengxin Chen, Xue-Zhi Li, Canrong Tian
This paper explores the spatiotemporal dynamics of a three-component predator–prey model with prey-taxis. We mainly show the existence of the steady state bifurcation and the bifurcating solution. Of most interesting discovery is that only the repulsive type prey-taxis could establish the existence of the steady state bifurcation and spatial pattern formation of the system. There are no steady state
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Local modification and analysis of a variable-order fractional wave equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-12 Shuyu Li, Hong Wang, Jinhong Jia
We investigate a local modification of a variable-order time-fractional wave equation, which models the vibrations of a viscoelastic bar along its longitudinal axis. Under suitable assumptions regarding the variable order at t=0, we prove that the original model is equivalent to a multiscale wave equation. Furthermore, we analyze the well-posedness of its weak solution. Numerical experiments are implemented
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Global [formula omitted]-estimates and dissipative [formula omitted]-estimates of solutions for retarded reaction–diffusion equations Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-10 Ruijing Wang, Chunqiu Li
This paper is concerned with the retarded reaction–diffusion equation ∂tu−Δu=f(u)+G(t,ut)+h(x) in a bounded domain. We allow both the nonlinear terms f and G to be supercritical, in which case the solutions may blow up in finite time, making it difficult to obtain global estimates. Here we employ some appropriate structure conditions to deal with this problem. In particular, we establish detailed global
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Acceleration of self-consistent field iteration for Kohn–Sham density functional theory Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-09 Fengmin Ge, Fusheng Luo, Fei Xu
Density functional theory calculations involve complex nonlinear models that require iterative algorithms to obtain approximate solutions. The number of iterations directly affects the computational efficiency of the iterative algorithms. However, for complex molecular systems, classical self-consistent field iterations either do not converge, or converge slowly. To improve the efficiency of self-consistent
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A quadrature formula on triangular domains via an interpolation-regression approach Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-06 Francesco Dell’Accio, Francisco Marcellán, Federico Nudo
In this paper, we present a quadrature formula on triangular domains based on a set of simplex points. This formula is defined via the constrained mock-Waldron least squares approximation. Numerical experiments validate the effectiveness of the proposed method.
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Dbar-dressing method for a new [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation Appl. Math. Lett. (IF 2.9) Pub Date : 2024-12-05 Zhenjie Niu, Biao Li
The primary purpose of this work is to consider a (2+1)-dimensional generalized KP equation via ∂̄-dressing method. Using the Fourier transform and Fourier inverse transform, we give the expression of the Green function for spatial spectral problem. Then, we choose two linear independent eigenfunctions and calculate the ∂̄ derivative, a ∂̄ problem arises naturally. Based on the symmetry of the Green