Mathematical Methods in the Applied Sciences最新文献_第2页

An approximate solution for stochastic Fitzhugh–Nagumo partial differential equations arising in neurobiology models 神经生物学模型中出现的随机 Fitzhugh-Nagumo 偏微分方程的近似解法

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-17 DOI: 10.1002/mma.10471

D. Uma, H. Jafari, S. Raja Balachandar, S. G. Venkatesh, S. Vaidyanathan

引用次数: 0

Similarity and consimilarity of hyper‐dual generalized quaternions 超二元广义四元数的相似性和相通性

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-17 DOI: 10.1002/mma.10488

Yasemin Alagöz, Gözde Özyurt

引用次数: 0

Uniform exponential stability approximations of semi‐discretization schemes for two hybrid systems 两个混合系统半离散化方案的统一指数稳定性近似值

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-14 DOI: 10.1002/mma.10484

Lu Zhang, Fu Zheng, Sizhe Wang, Zhongjie Han

{"title":"Uniform exponential stability approximations of semi‐discretization schemes for two hybrid systems","authors":"Lu Zhang, Fu Zheng, Sizhe Wang, Zhongjie Han","doi":"10.1002/mma.10484","DOIUrl":"https://doi.org/10.1002/mma.10484","url":null,"abstract":"The uniform exponential stabilities (UESs) of two hybrid control systems comprised of a wave equation and a second‐order ordinary differential equation are investigated in this study. Linear feedback law and local viscosity are considered, as are nonlinear feedback law and internal anti‐damping. The hybrid system is first reduced to a first‐order port‐Hamiltonian system with dynamical boundary conditions, and the resulting system is discretized using the average central‐difference scheme. Second, the UES of the discrete system is obtained without prior knowledge of the exponential stability of the continuous system. The frequency domain characterization of UES for a family of contractive semigroups and the discrete multiplier approach are used to validate the main conclusions. Finally, the Trotter–Kato theorem is used to perform a convergence study on the numerical approximation approach. Most notably, the exponential stability of the continuous system is derived by the convergence of energy and UES, which is a novel approach to studying the exponential stability of some complex systems. Numerical simulation is used to validate the effectiveness of the numerical approximating strategy.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A new representation for the solution of the Richards‐type fractional differential equation 理查兹型分数微分方程解法的新表示法

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-13 DOI: 10.1002/mma.10394

Iz‐iddine EL‐Fassi, Juan J. Nieto, Masakazu Onitsuka

引用次数: 0

Clifford‐valued linear canonical wavelet transform and the corresponding uncertainty principles 克利福德值线性小波变换和相应的不确定性原理

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI: 10.1002/mma.10468

Shahbaz Rafiq, Mohammad Younus Bhat

引用次数: 0

Pattern dynamics in a water–vegetation model with cross‐diffusion and nonlocal delay 具有交叉扩散和非局部延迟的水-植被模型中的模式动力学

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI: 10.1002/mma.10480

Gaihui Guo, Jing You, Khalid Ahmed Abbakar

引用次数: 0

Viscoelasticity, logarithmic stresses, and tensorial transport equations 粘弹性、对数应力和张量传输方程

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI: 10.1002/mma.10469

Gennaro Ciampa, Giulio G. Giusteri, Alessio G. Soggiu

{"title":"Viscoelasticity, logarithmic stresses, and tensorial transport equations","authors":"Gennaro Ciampa, Giulio G. Giusteri, Alessio G. Soggiu","doi":"10.1002/mma.10469","DOIUrl":"https://doi.org/10.1002/mma.10469","url":null,"abstract":"We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally belong to a multiplicative group of linear transformations, to stresses, that are additive elements of a linear space of tensors. As regards the viscous stresses, we simply assume a Newtonian constitutive law, but the presence of elasticity and plastic relaxation makes the materials non‐Newtonian. Our aim is to discuss the existence of weak solutions for the corresponding systems of partial differential equations in the nonlinear large‐deformation regime. The main difficulties arise in the analysis of the transport equations necessary to describe the evolution of tensorial measures of strain. For the solid model, we only need to consider the equation for the left Cauchy–Green tensor, while for the fluid model, we add an evolution equation for the elastically‐relaxed strain. Due to the tensorial nature of the fields, available techniques cannot be applied to the analysis of such transport equations. To cope with this, we introduce the notion of charted weak solution, based on non‐standard a priori estimates, that lead to a global‐in‐time existence of solutions for the viscoelastic models in the natural functional setting associated with the energy inequality.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability analysis and error estimation based on difference spectral approximation for Allen–Cahn equation in a circular domain 基于圆域中艾伦-卡恩方程差分谱近似的稳定性分析和误差估计

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI: 10.1002/mma.10481

Zhenlan Pan, Jihui Zheng, Jing An

引用次数: 0

Exponential stability of a class of quaternion‐valued memristor‐based neural network with time‐varying delay via M‐matrix 通过 M 矩阵实现一类基于四元数值忆阻器的时变延迟神经网络的指数稳定性

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-11 DOI: 10.1002/mma.10486

Shengye Wang, Yanchao Shi, Jun Guo

引用次数: 0

Bayesian inversion of a fractional elliptic system derived from seismic exploration 对地震勘探得出的分数椭圆系统进行贝叶斯反演

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-10 DOI: 10.1002/mma.10474

Yujiao Li

{"title":"Bayesian inversion of a fractional elliptic system derived from seismic exploration","authors":"Yujiao Li","doi":"10.1002/mma.10474","DOIUrl":"https://doi.org/10.1002/mma.10474","url":null,"abstract":"In this paper, we concentrate on the Bayesian inversion of a dispersion‐dominated fractional Helmholtz (DDFH) equation, which has been introduced in studies concerning seismic exploration. To establish the inversion theory, we meticulously examine the DDFH equation. We transform it into a system comprising both fractional‐ and integer‐order elliptic equations, extending the conventional definition of the spectral fractional Laplace operator to accommodate non‐homogeneous boundary conditions. Subsequently, we establish the well‐posedness theory for scenarios involving both small and large wavenumbers. Our proof hinges upon the regularity attributes of select fractional elliptic equations and capitalizes fully on the structural peculiarities of the elliptic system, which distinguish it from classical cases. Thereafter, we focus on the inverse medium scattering problem pertinent to the DDFH equation, framed within the Bayesian statistical framework. We address two scenarios: one devoid of model reduction errors and another characterized by such errors—arising from the implementation of certain absorbing boundary conditions. More precisely, based on the properties of the forward operator, well‐posedness of the posterior measures have been proved in both cases, which provide an opportunity to quantify the uncertainties of this problem.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0