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Normalized solutions to the Kirchhoff Equation with triple critical exponents in [formula omitted] Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-12 Xingling Fang, Zengqi Ou, Ying Lv
In this paper, we investigate the normalized solutions for the nonlinear critical Kirchhoff equations with combined nonlinearities: where , , and , , are constants. In , some interesting phenomena occur, which are, the -critical exponent for is , while the -critical exponent for is equal to the Sobolev critical exponent, i.e., . This paper investigates the case that the nonlinearity with triple critical
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Total and scattered field decomposition technique in mixed FETD methods and its applications for electromagnetic cloaks Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-12 Fuhao Liu, Wei Yang
In this paper, we apply the total and scattered field plane wave excitation method to the mixed finite element time-domain (FETD) method for solving Maxwell’s equations to compute the scattered field of electromagnetic cloaks. This method can quantify the performance and operating frequency range of the cloak. We also present a mixed FETD scheme, which is coupling with perfectly matched layers technique
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Positive solutions of parameter-dependent nonlocal differential equations with convolution coefficients Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-11 Xinan Hao, Xuhui Wang
In this paper we investigate a parameter-dependent nonlocal differential equations with convolution coefficients. Using the Birkhoff-Kellogg type theorem, existence of positive solutions is established. Under additional growth conditions, we obtain upper and lower bounds for the parameter. An example is also given to illustrate the main results.
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An energy estimate and a stabilized Lagrange–Galerkin scheme for a multiphase flow model Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-11 Aufa Rudiawan, Alexander Žák, Michal Beneš, Masato Kimura, Hirofumi Notsu
Multiphase flow models are commonly employed for understanding complex fluid flows, while few mathematical discussions exist. For a general multiphase flow model in Gidaspow (1994), an energy decay property is proved. A stabilized Lagrange–Galerkin scheme for the model and its stability property are presented. Here, a hyperbolic tangent transformation is employed to preserve the boundedness of the
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The (2+1)-dimensional generalized Benjamin–Ono equation: Nonlocal symmetry, CTE solvability and interaction solutions Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-11 Yueying Wu, Yunhu Wang
In this paper, the nonlocal symmetry of the (2+1)-dimensional generalized Benjamin–Ono equation are obtained by using the truncated Painlevé expansion. The nonlocal symmetry are localized by introducing auxiliary variables. Furthermore, this equation is also proved to be consistent expansion solvable, and three classes of exact solutions are derived.
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Oscillation of second-order trinomial differential equations with retarded and advanced arguments Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-07 Jozef Dzurina
In this paper we introduce new effective technique for investigation of oscillation for the second-order trinomial differential equation with retarded and advanced arguments Our criteria improve the existing ones and the progress is illustrated via several examples.
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A new kernel method for the uniform approximation in reproducing kernel Hilbert spaces Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-06 Woula Themistoclakis, Marc Van Barel
We are concerned with the uniform approximation of functions of a generic reproducing kernel Hilbert space (RKHS). In this general context, classical approximations are given by Fourier orthogonal projections (if we know the Fourier coefficients) and their discrete versions (if we know the function values on well-distributed nodes). In case such approximations are not satisfactory, we propose to improve
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Dispersive shock wave structure analysis for the defocusing Lakshmanan–Porsezian–Daniel equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-04 Yan Zhang, Hui-Qin Hao
Via the finite-gap integration theory, we study the defocusing Lakshmanan–Porsezian–Daniel (LPD) equation. Meanwhile, we derive the degenerate forms for the single-phase periodic solution. In addition, we obtain the basic and combined structures of the dispersive shock wave through the Whitham modulation equation parameterized by the Riemann invariant.
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Stability of impulsive stochastic functional differential equations with delays Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-04 Jingxian Guo, Shuihong Xiao, Jianli Li
In this paper, we consider the global asymptotical stability of stochastic functional differential equations with impulsive effects. First, by constructing the Lyapunov function, some stability criteria of impulsive stochastic functional differential equations are established. Second, we propose an application to investigate the effectiveness of the obtained results.
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A greedy average block sparse Kaczmarz method for sparse solutions of linear systems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-04 A-Qin Xiao, Jun-Feng Yin
A greedy average block sparse Kaczmarz method is developed for the sparse solution of the linear system of equations. The convergence theory of this method is established and the upper bound of its convergence rate with adaptive stepsize is derived. Numerical experiments are presented to verify the efficiency of the proposed method, which outperforms the existing sparse Kaczmarz methods in terms of
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Mass and energy conservative high-order diagonally implicit Runge–Kutta schemes for nonlinear Schrödinger equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-04 Ziyuan Liu, Hong Zhang, Xu Qian, Songhe Song
We present and analyze a series of structure-preserving diagonally implicit Runge–Kutta schemes for the nonlinear Schrödinger equation. These schemes possess not only high accuracy, high order convergence (up to fifth order) and efficiency due to the diagonally implicity but also mass and energy conservative properties. Theoretical analysis and numerical experiments are conducted to verify the accuracy
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Global existence for the stochastic rotation-two-component Camassa–Holm system with nonlinear noise Appl. Math. Lett. (IF 3.7) Pub Date : 2024-03-01 Yeyu Xiao, Yong Chen
We study the well-posedness for the stochastic rotation-two-component Camassa–Holm (R2CH) system with the nonlinear noise. We establish the local well-posedness of the stochastic R2CH system by the dispersion–dissipation approximation system and the regularization method. We also prove the global existence of the stochastic R2CH system with a large nonlinear noise.
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Stationary distribution analysis of a stochastic SIAM epidemic model with Ornstein–Uhlenbeck process and media coverage Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-28 Yilin Tian, Chao Liu, Lora Cheung
A stochastic SIAM (Susceptible individual-Infected individual-Aware individual-Media coverage) epidemic model with nonlinear disturbances is constructed, where awareness dissemination rate satisfies the mean-reverting Ornstein–Uhlenbeck process. Hybrid dynamic effects of Lévy jump and Ornstein–Uhlenbeck process on infectious disease transmission are discussed. By constructing appropriate stochastic
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Well-posedness for the stochastic Landau–Lifshitz–Bloch equation with helicity Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-27 Soham Sanjay Gokhale
We consider the stochastic Landau-Lifshitz-Bloch equation with helicity term driven by a real-valued Wiener process. We show the existence of a weak martingale solution, followed by pathwise uniqueness of the obtained solution, culminating into the existence of a strong solution using the theory of Yamada and Watanabe.
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The composite wave in the Riemann solutions for macroscopic production model Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-27 Zhijian Wei, Lihui Guo
In this paper, the Riemann solutions for the macroscopic production model with chaplygin gas under some special initial data are constructively obtained in the fully explicit form. An interesting composite wave is observed, it is formed by a rarefaction wave and a left-contact delta discontinuity attached to the wavefront of the rarefaction wave. Furthermore, this delta discontinuity gradually absorbs
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Sixth-order exponential Runge–Kutta methods for stiff systems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-27 Vu Thai Luan, Trky Alhsmy
This work constructs the first-ever sixth-order exponential Runge–Kutta (ExpRK) methods for the time integration of stiff parabolic PDEs. First, we leverage the exponential B-series theory to restate the stiff order conditions for ExpRK methods of arbitrary order based on an essential set of trees only. Then, we explicitly provide the 36 order conditions required for sixth-order methods and present
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The stabilized exponential-SAV approach for the Allen–Cahn equation with a general mobility Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-23 Yuelong Tang
In this paper, we construct a second-order accurate, energy stable and maximum bound principle-preserving scheme for the Allen–Cahn equation with a general mobility based on the stabilized exponential scalar auxiliary variable (SESAV) approach. Some extra stabilizing terms are added to the discretized scheme for the purpose of improving numerical stability. We first proved the maximum bound principle
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New Liouville-type theorem for the stationary tropical climate model Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-23 Youseung Cho, Hyunjin In, Minsuk Yang
We study the Liouville-type theorem for smooth solutions to the steady 3D tropical climate model. We prove the Liouville-type theorem if a smooth solution satisfies a certain growth condition in terms of -norm on annuli, which improves the previous results, Theorem 1.1 by Ding and Wu (2021), and Theorem 1.1 and Theorem 1.2 by Yuan and Wang (2023).
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Asymptotic analysis of time-fractional quantum diffusion Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-23 Peter D. Hislop, Éric Soccorsi
We study the large-time asymptotics of the mean-square displacement for the time-fractional Schrödinger equation in . We define the time-fractional derivative by the Caputo derivative. We consider the initial-value problem for the free evolution of wave packets in governed by the time-fractional Schrödinger equation , with initial condition , parameterized by two indices . We show distinctly different
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Global solvability for an indirect consumption chemotaxis system with signal-dependent motility Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-22 Ai Huang, Yifu Wang
This paper considers the indirect signal consumption-chemotaxis system with signal-dependent motility in a smooth bounded domain , as given by , where the motility function on , which generalizes . Based on point-wise positive lower bound estimate of , it is shown that for any suitably regular initial data, the corresponding initial–boundary value problem admits global smooth solutions.
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Dynamics for the diffusive logistic equation with a sedentary compartment and free boundary Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-22 Xueping Li, Lei Li, Mingxin Wang
This paper investigates the diffusive logistic equation with a sedentary compartment and free boundary whose dynamics has been considered by Wang and Cao (2015) when the intrinsic rate of reproduction in the stationary class is less than the rate of switching from stationary to mobile. However, the case is left as an open problem in Wang and Cao (2015). We shall show that spreading happens if and give
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Nonlocal symmetry and group invariant solutions of dissipative (2+1)-dimensional AKNS equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-21 Yarong Xia, Jiayang Geng, Ruoxia Yao
In this paper, the nonlocal symmetry of dissipative (2+1)-dimensional AKNS equation is constructed by auxiliary equation method. In order to better study new group invariant solutions of AKNS equation with the help of nonlocal symmetry, we introduce an new auxiliary dependent variable, the (2+1) dimensional AKNS equation is extended to a new closed prolonged system. Therefore, the nonlocal symmetry
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Periodic transmission theory of circularly symmetric multi-ring solitons in nonlinear Schrödinger equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-21 Jie Li, Zhi-Ping Dai, Zhen-Jun Yang
In this paper, the evolution characteristics of periodic transmission of circularly symmetric multi-ring solitons in optical nonlocal materials based on nonlinear Schrödinger equation are investigated in detail. The transmission expression of circularly symmetric multi-ring solitons has been derived. It was found that the number and size of rings in these solitons can be controlled by initial parameters
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Long-time asymptotics for the integrable nonlocal Lakshmanan–Porsezian–Daniel equation with decaying initial value data Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-20 Wei-Qi Peng, Yong Chen
In this work, we study the Cauchy problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation with rapid attenuation of initial data. The basic Riemann–Hilbert problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation is constructed from Lax pair. Using Deift-Zhou nonlinear steepest descent method, the explicit long-time asymptotic formula of integrable nonlocal Lakshmanan-Porsezian-Daniel
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Inverse scattering and soliton dynamics for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-20 Nan Liu, Jinyi Sun, Jia-Dong Yu
Under investigation in this letter is a mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation which can be considered as the simplest model to approximate the dynamics of weakly nonlinear and dispersive waves, taking into account the self-steepening effect. The inverse scattering transform under the zero boundary conditions and analytical scattering coefficients with an arbitrary number of simple
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A randomized block extended Kaczmarz method with hybrid partitions for solving large inconsistent linear systems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-20 Xiang-Long Jiang, Ke Zhang
We propose a randomized block extended Kaczmarz method with hybrid partitioning techniques for solving large inconsistent linear systems. It employs the -means clustering to partition the columns of the coefficient matrix while applying the uniform sampling to derive the row partition of the coefficient matrix. It is proved that the proposed algorithm converges to the unique least-squares least-norm
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Novel criterion for the existence of solutions with positive coordinates to a system of linear delayed differential equations with multiple delays Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-19 Josef Diblík
A linear system of delayed differential equations with multiple delays is considered where is an -dimensional column vector, , is a fixed integer, delays are positive and bounded, entries of by matrices as well as functions are nonnegative, and the sums of columns of the matrix are identical and equal to a function . It is proved that, on , the system has a solution with positive coordinates if and
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Support set and unique ergodicity of stochastic KdV equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-19 Shang Wu, Jianhua Huang
This paper presents the support set and unique ergodicity of invariant measure given in Ekren (2018) of stochastic KdV equation, which also offers an answer to the question about support set raised in Wu (2023). To begin with, we investigate the exponential decay of the norm of the solution. Subsequently, we employ the truncated method in conjunction with the dominated convergence theorem to prove
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A four-component hierarchy of combined integrable equations with bi-Hamiltonian formulations Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-15 Wen-Xiu Ma
Upon introducing a specific 4 × 4 matrix eigenvalue problem with four components, we would like to construct a Liouville integrable Hamiltonian hierarchy, within the zero curvature formulation. Bi-Hamiltonian formulations are furnished via the trace identity, through which the Liouville integrability of the resulting hierarchy is explored. The first two nonlinear examples are novel generalized combined
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The exact solutions for the non-isospectral Kaup–Newell hierarchy via the inverse scattering transform Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-14 Hongyi Zhang, Yufeng Zhang, Binlu Feng, Faiza Afzal
We begin by introducing a non-isospectral Lax pair, from which we derive a non-isospectral integrable Kaup–Newell hierarchy. The new general solutions for the non-isospectral integrable Kaup–Newell hierarchy are obtained through the inverse scattering transform (IST) method. Finally, we obtain the soliton solutions of a reduced non-isospectral integrable equation from non-isospectral integrable Kaup–Newell
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Radial symmetric normalized solutions for a singular elliptic equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-14 Pengfei He, Hongmin Suo
In this paper, we are concerned with the existence of radial symmetric normalized solutions of a singular elliptic equation, and we investigate the damped behavior of normalized solutions.
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Conditional regularity for the 3D magnetic Bénard system in Vishik spaces Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-13 Dandan Ma, Andrea Scapellato, Fan Wu
In this paper, we consider the Cauchy problem associated to a magnetic Bénard system in . By using Littlewood-Paley decomposition technique, we provide regularity criteria involving the gradient of the velocity in Vishik spaces, which generalize some well-known results.
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Novel Lax pair and many conservation laws to a [formula omitted]-dimensional generalized combined Calogero–Bogoyavlenskii–Schiff-type equation in biohydrodynamics Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-13 Ting-Ting Jia, Ya-Juan Li, Gang Yang
Under investigation in this paper is a -dimensional generalized combined Calogero–Bogoyavlenskii–Schiff-type equation for certain nonlinear phenomena in biohydrodynamics, fluids and plasmas. A novel differential form Lax pair with certain conditions is constructed with an arbitrary function , while an iterative operator different from those in the existing literatures is derived and fully verified
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Lower and upper bounds of the solution for the Lyapunov matrix differential equation and an application in input-output finite-time stability of linear systems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-09 Jianzhou Liu, Ze Zhang, Yan Xu
In control theory and practical engineering fields, such as the controllability, observability, input–output finite-time stability of the linear systems, it is a significant problem to study the properties of the solution for the Lyapunov matrix differential equation where there are no restrictions on the system matrix. In this paper, by constructing an equivalent form of the Lyapunov matrix differential
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A new method of solving the Riesz fractional advection–dispersion equation with nonsmooth solution Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-08 Hong Du, Zhong Chen
The Riesz fractional advection–dispersion equation with weak singularities at boundaries is solved. Our important contributions are to propose a new approach, construct successfully the fractional polynomial approximate functions with weak singularities at both endpoints in spatial direction, provide the minimum residual solution (MRS) and convergence order. Numerical examples show that the proposed
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Two-layer-liquid and lattice considerations through a (3+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama system Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-07 Xin-Yi Gao
Current studies on the liquids and lattices attract people’s attention. In this Letter, for certain interfacial waves in a two-layer liquid or elastic waves in a lattice, we investigate a (3+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama system via building a set of the similarity reductions. In respect of the amplitude or elevation of the relevant wave, our similarity reductions are from that system
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Dual quaternion singular value decomposition based on bidiagonalization to a dual number matrix using dual quaternion householder transformations Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-07 Wenxv Ding, Ying Li, Tao Wang, Musheng Wei
We propose a practical method for computing the singular value decomposition of dual quaternion matrices. The dual quaternion Householder matrix is first proposed, and by combining the properties of dual quaternions, we can implement the transformation of a dual quaternion matrix to a bidiagonalized dual number matrix. We have proven that the singular values of a dual quaternion matrix are same to
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Improved results on normalized solutions for planar Schrödinger–Poisson equations with [formula omitted]-supercritical case Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-07 Jiuyang Wei, Muhua Shu
We prove the existence of normalized solutions for the following planar Schrödinger–Poisson equation where , and arises as a Lagrange multiplier and is not a priori given. In the axially symmetric setting, new variational techniques and inequalities related with logarithmic convolution potential are developed to detect the geometry structure of the constrained functional, we believe, which can be applicable
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Polynomial approximation of derivatives through a regression–interpolation method Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-06 Francesco Dell’Accio, Federico Nudo
The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge phenomenon that occurs when using polynomial interpolation on large sets of equally spaced points. The idea is to improve the mock-Chebyshev subset interpolation
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A new meshless method of solving the distributed-order time-fractional mobile-immobile equations Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-05 Jian Zhang, Xinyue Yang, Wei Song
A new method is introduced by combining neural network’s huge expressive power with technologies of the minimum residual approximate solutions (MRASs). In spatial direction, a single hidden layer neural network makes the construction of bases functions easier. The cost of calculations becomes acceptable in high dimensions space using the technologies of the MRASs. And this paper establish approximation
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A note on progressive hedging algorithm for multistage stochastic variational inequalities Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-03 Xihong Yan, Chuanlong Wang, Junfeng Yang
(PHA) is a long-standing algorithm originally designed for stochastic programming problems and has recently been extended to solving multistage (SVIs), both are important tools for processing mathematical programming problems with uncertainty. In this note, we first show that PHA for two-stage stochastic linear complementarity problems, a special case of multistage SVIs, is an application of the Douglas-Rachford
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Determination of equilibrium parameters of the Marle model for polyatomic gases Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-03 Byung-Hoon Hwang
The BGK model is a relaxation-time approximation of the celebrated Boltzmann equation, and the Marle model is a direct extension of the BGK model in a relativistic framework. In this paper, we introduce the Marle model for polyatomic gases based on the Jüttner distribution devised in [Ann. Phys., 377, (2017), 414–445], and show the existence of a unique set of equilibrium parameters of the Jüttner
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The spreading speed of single-species models with resource-dependent dispersal and a free boundary Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-30 Dawei Zhang, Chufen Wu
In this paper, we study the spreading speed of single-species models with resource-dependent dispersal and a free boundary, which describe the propagation process of an invasive species in a spatially heterogeneous environment. To overcome the analytical difficulties brought by the resource-dependent dispersal, we use an idea of changing variables to transform the above models into the uniform dispersal
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A BDF3 and new nonlinear fourth-order difference scheme for the generalized viscous Burgers’ equation Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-30 Jiawei Wang, Xiaoxuan Jiang, Haixiang Zhang
This study explores a third-order backward differentiation formula (BDF3) and nonlinear fourth-order difference method (FODM) for solving the generalized viscous Burgers’ equation (GVBE). The BDF3 method is employed for discretizing the time derivative, while the nonlinear term uλux is handled using a newly constructed nonlinear fourth-order difference operator. The spatial second derivative is discretized
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Solving a fractional chemotaxis system with logistic source using a meshless method Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-02 Antonio M. Vargas
We study the numerical solution of the fractional Keller–Segel system with logistic source. We derive the discretization of the fractional Laplacian and integer derivatives using a meshless method. A condition for convergence is given and several examples illustrating the dynamics of both fully parabolic and parabolic–elliptic systems on irregular meshes are provided.
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Extending matrix–vector framework on multiple relaxation time lattice Boltzmann method Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-02 Reza MohammadiArani, Mehdi Dehghan, Mostafa Abbaszadeh
This paper introduces an extension of a fully discrete matrix–vector form (MVF) for the lattice Boltzmann method (LBM) to handle the multiple relaxation time parameter (MRT) LBM. The proposed approach offers a more efficient and practical framework for simulating fluid flows, with the added benefit of being able to handle complex geometries using the image-based ghost (IBG) method. The advantages and
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N-soliton solutions for the three-component Dirac–Manakov system via Riemann–Hilbert approach Appl. Math. Lett. (IF 3.7) Pub Date : 2024-02-02 Yuxia Wang, Lin Huang, Jing Yu
This investigation delves into the application of the well-established Riemann–Hilbert method for the elucidation of the N-solitons solution of the three-component Dirac–Manakov system. The analytical process is structured in two fundamental steps. Initially, the inverse scattering method is employed to establish a pivotal connection between the solution of the three-component DiracManakov system and
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Generalized Heisenberg equations and bi-Hamiltonian structures Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-24 Yihao Li, Minxin Jia, Jiao Wei
By introducing a 3 × 3 matrix spectral problem, a hierarchy of generalized Heisenberg equations is derived with the aid of the zero-curvature equation. The bi-Hamiltonian form for the hierarchy of generalized Heisenberg equations is established by using the trace identity. Furthermore, we construct the infinite conservation laws of the first nontrivial equation in the hierarchy by means of spectral
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Asymptotically linear magnetic fractional problems Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-28 Rossella Bartolo, Pietro d’Avenia, Giovanni Molica Bisci
The aim of this paper is investigating the existence and multiplicity of weak solutions to non-local equations involving the magnetic fractional Laplacian, when the nonlinearity is subcritical and asymptotically linear at infinity. We prove existence and multiplicity results by using variational tools, extending to the magnetic local and non-local setting some known results for the classical and the
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The subsonic or sonic–subsonic solution of the electric potential driven problem to the HD model for semiconductors Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-24 Siying Li, Kaijun Zhang, Guojing Zhang
This paper concerns the stationary subsonic or sonic–subsonic solution of the electric potential driven problem to the isentropic hydrodynamic model for semiconductors. We give a necessary and sufficient condition to ensure the existence of this kind of solution. Specifically, there exists a subsonic or sonic–subsonic solution to this problem if and only if 0≤ϕr≤ϕ̄, with the number ϕ̄=O1τ. Here, ϕr
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Global stability and Hopf bifurcation of networked respiratory disease model with delay Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-28 Lei Shi, Jiaying Zhou, Yong Ye
Time delay is introduced into a networked respiratory disease model, which describes the occurrence of respiratory diseases caused by air pollution. By analyzing the eigenvalues, it has been proven that when the delay exceeds the threshold, the endemic equilibrium loses stability through Hopf bifurcation. In addition, employing Lyapunov functions, we provide the condition that the endemic equilibrium
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Global well-posedness to the 3D incompressible magneto-micropolar Bénard system with damping and zero thermal conductivity Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-22 Xiaohua Shou, Xin Zhong
We are concerned with the three-dimensional (3D) Cauchy problem of the incompressible magneto-micropolar Bénard system with a nonlinear damping term α|u|β−1u(α>0andβ≥1) in the momentum equations. By energy method, we derive a unique global strong solution for such a model when β≥4. Our result extends previous related works.
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Global classical solutions of a nonlinear consumption system with singular density-suppressed motility Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-20 Zhiguang Zhang, Yuxiang Li
In this note, we study the no-flux initial-boundary value problem for the migration-consumption taxis system involving singular density-suppressed motility (⋆)ut=Δ((u+1)lϕ(v)),vt=Δv−uvmin a bounded smooth domain Ω⊂Rn (n⩾2), where ϕ generalizes the singular prototype given by ϕ(ξ)=ξ−α (ξ>0) with α>0. We prove that if l>n2 and m⩾1, then the model (⋆) possesses a global classical solution.
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Numerical analysis of growth-mediated autochemotactic pattern formation in self-propelling bacteria Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-15 Maosheng Jiang, Jiang Zhu, Xijun Yu, Luiz Bevilacqua
In this letter, a decoupled characteristic Galerkin finite element procedure is provided for simulating growth-mediated autochemotactic pattern formation in self-propelling bacteria. In this procedure, a modified characteristic Galerkin method is established to solve the bacterial density equation, while the finite element procedure is considered for the self-secreted chemical density and polarization
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Finite element approximation and analysis of damped viscoelastic hyperbolic integrodifferential equations with L1 kernel Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-15 Mingchao Zhao, Wenlin Qiu
In this paper, we propose a finite element method for solving viscoelastic hyperbolic integrodifferential equations with L1 kernel, involving a nonlocal and nonlinear damped coefficient. Firstly, we discuss and deduce that the L1 kernel is of positive type in two cases. Subsequently, based on the continuous Galerkin technique and the energy argument, we prove the global existence and uniqueness of
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Supercloseness of the LDG method for a singularly perturbed convection–diffusion problem on Bakhvalov-type mesh Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-08 Chunxiao Zhang, Jin Zhang, Wenchao Zheng
In this study, the focus is on exploring the supercloseness property of the local discontinuous Galerkin (LDG) method in the context of a singularly perturbed convection–diffusion problem on Bakhvalov-type mesh. By developing specialized local Gauss–Radau projections in the two-dimensional case, and establishing a novel interpolation premised on the special projections, supercloseness of an optimal
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An improved result for a three-species spatial food chain model Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-09 Changchun Liu, Dongze Yan
This paper is a further step in the study of the existence. The purpose is to enhance the results of the paper (Jin et al., 2022). We will improve the spatial dimensions from 2 to any space dimension n.
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An extended Merola–Ragnisco–Tu lattice integrable hierarchy and infinite conservation laws Appl. Math. Lett. (IF 3.7) Pub Date : 2024-01-09 Xin Wang
By means of the zero-curvature equation and Lenard recursive operators, a novel differential-difference integrable hierarchy is derived, which is related to a discrete 3 × 3 matrix spectral problem with five potentials. The first nontrivial member in this hierarchy under specific reduction is the Merola–Ragnisco–Tu lattice equation whose continuum limit is the nonlinear Schrödinger equation. The infinite