Journal of Integral Equations and Applications最新文献_第3页

FIXED-POINT THEOREMS FOR MEIR–KEELER MULTIVALUED MAPS AND APPLICATION MEIR&KEELER多值映射的不动点定理及其应用

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-12-01 DOI: 10.1216/jie.2022.34.389

Maha Belhadj, Jamal Rezaei Roshan, Mohamed Boumaiza, Vahid Parvaneh

引用次数: 0

SOLVABILITY AND APPROXIMATION OF NONLINEAR FUNCTIONAL MIXED VOLTERRA–FREDHOLM EQUATION IN BANACH SPACE BANACH空间中非线性泛函混合VOLTERRA&FREDHOLM方程的可解性与逼近

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-12-01 DOI: 10.1216/jie.2022.34.489

C. Nwaigwe

引用次数: 3

MIXED BOUNDARY VALUE PROBLEMS FOR THE HELMHOLTZ EQUATION 亥姆霍兹方程的混合边值问题

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-12-01 DOI: 10.1216/jie.2022.34.475

D. Natroshvili, T. Tsertsvadze

引用次数: 0

INVERSE NODAL PROBLEM FOR THE INTEGRODIFFERENTIAL DIRAC OPERATOR WITH A DELAY IN THE KERNEL 核中有时滞的积分微分狄拉克算子的逆节点问题

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-12-01 DOI: 10.1216/jie.2022.34.465

S. Mosazadeh

引用次数: 0

CONTROLLABILITY OF SEMILINEAR NEUTRAL STOCHASTIC INTEGRODIFFERENTIAL EVOLUTION SYSTEMS WITH FRACTIONAL BROWNIAN MOTION 具有分数阶布朗运动的半线性中性随机积分微分演化系统的可控性

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-12-01 DOI: 10.1216/jie.2022.34.409

Nan Cao, Xianlong Fu

引用次数: 0

REGULARITY OF SOLUTIONS FOR NONLOCAL DIFFUSION EQUATIONS ON PERIODIC DISTRIBUTIONS 周期分布上非局部扩散方程解的正则性

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-09-23 DOI: 10.1216/jie.2023.35.81

I. Mustapha, Bacim Alali, Nathan Albin

{"title":"REGULARITY OF SOLUTIONS FOR NONLOCAL DIFFUSION EQUATIONS ON PERIODIC DISTRIBUTIONS","authors":"I. Mustapha, Bacim Alali, Nathan Albin","doi":"10.1216/jie.2023.35.81","DOIUrl":"https://doi.org/10.1216/jie.2023.35.81","url":null,"abstract":"This work addresses the regularity of solutions for a nonlocal diffusion equation over the space of periodic distributions. The spatial operator for the nonlocal diffusion equation is given by a nonlocal Laplace operator with a compactly supported integral kernel. We follow a unified approach based on the Fourier multipliers of the nonlocal Laplace operator, which allows the study of regular as well as distributional solutions of the nonlocal diffusion equation, integrable as well as singular kernels, in any spatial dimension. In addition, the results extend beyond operators with singular kernels to nonlocal super-diffusion operators. We present results on the spatial and temporal regularity of solutions in terms of regularity of the initial data or the diffusion source term. Moreover, solutions of the nonlocal diffusion equation are shown to converge to the solution of the classical diffusion equation for two types of limits: as the spatial nonlocality vanishes or as the singularity of the integral kernel approaches a certain critical singularity that depends on the spatial dimension. Furthermore, we show that, for the case of integrable kernels, discontinuities in the initial data propagate and persist in the solution of the nonlocal diffusion equation. The magnitude of a jump discontinuity is shown to decay overtime.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43840927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1

Positivity of a weakly singular operator and approximation of wave scattering from the sphere 弱奇异算子的正性与球面波散射的近似

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-09-01 DOI: 10.1216/jie.2022.34.317

D. Duncan

{"title":"Positivity of a weakly singular operator and approximation of wave scattering from the sphere","authors":"D. Duncan","doi":"10.1216/jie.2022.34.317","DOIUrl":"https://doi.org/10.1216/jie.2022.34.317","url":null,"abstract":"We investigate properties of a family of integral operators B with a weakly singular compactly supported zonal kernel function on the surface S of the unit 3D sphere. The support is over a spherical cap of height h ∈ (0,2]. Operators like this arise in some common types of approximations of time domain boundary integral equations (TDBIE) describing the scattering of acoustic waves from the surface of the sphere embedded in an infinite homogeneous medium where h is directly related to the time step size. We show that the Legendre polynomials of degree `≥ 0 satisfy ∫ h 0 P̀ (1−z2/2)dz > 0 for all h∈ (0,2] and, using spherical harmonics and the Funk-Hecke formula for the eigenvalues of B, that this is a key to unlocking positivity results for a subfamily of these operators. As well as positivity results we give detailed upper and lower bounds on the eigenvalues of B and on ∫ S u(x)(Bu)(x) dx. We give various examples of where these results are useful in numerical approximations of the TDBIE on the sphere and show that positivity of B is a necessary condition for these approximation schemes to be well-defined. We also show the connection between the results for eigenvalues and the separation of variables solution of the TDBIE on the sphere. Finally we show how this relates to scattering from an infinite flat surface and Cooke’s 1937 result ∫ r 0 J0(z)dz > 0 for all r > 0.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41696948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 numerical algorithm for a class of nonlinear fractional Volterra integral equations via modified hat functions 一类非线性分数阶Volterra积分方程的修正帽函数数值算法

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-09-01 DOI: 10.1216/jie.2022.34.295

J. Biazar, H. Ebrahimi

引用次数: 3

Optimal stability for a viscoelastic neutral differential problem 粘弹性中性微分问题的最优稳定性

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-09-01 DOI: 10.1216/jie.2022.34.335

J. Hassan, N. Tatar

引用次数: 0

Friction mediated by transient elastic linkages: extension to loads of bounded variation 瞬态弹性连杆机构介导的摩擦力：对有界变化载荷的扩展

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2022-09-01 DOI: 10.1216/jie.2022.34.267

S. Allouch, V. Milišić

引用次数: 1