Journal of Integral Equations and Applications最新文献_第9页

Solutions of second-order degenerate equations with infinite delay in Banach spaces Banach空间中具有无限延迟的二阶退化方程的解

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-09-01 DOI: 10.1216/jie.2020.32.259

Shangquan Bu, G. Cai

引用次数: 0

Mixed impedance boundary value problems for the Laplace–Beltrami equation Laplace-Beltrami方程的混合阻抗边值问题

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-09-01 DOI: 10.1216/jie.2020.32.275

L. Castro, R. Duduchava, F. Speck

{"title":"Mixed impedance boundary value problems for the Laplace–Beltrami equation","authors":"L. Castro, R. Duduchava, F. Speck","doi":"10.1216/jie.2020.32.275","DOIUrl":"https://doi.org/10.1216/jie.2020.32.275","url":null,"abstract":"This work is devoted to the analysis of the mixed impedance-Neumann-Dirichlet boundary value problem (MIND BVP) for the Laplace-Beltrami equation on a compact smooth surface C with smooth boundary. We prove, using the Lax-Milgram Lemma, that this MIND BVP has a unique solution in the classical weak setting H1(C) when considering positive constants in the impedance condition. The main purpose is to consider the MIND BVP in a nonclassical setting of the Bessel potential space Hp(C), for s > 1/p, 1 < p < ∞. We apply a quasilocalization technique to the MIND BVP and obtain model Dirichlet-Neumann, Dirichletimpedance and Neumann-impedance BVPs for the Laplacian in the half-plane. The model mixed Dirichlet-Neumann BVP was investigated by R. Duduchava and M. Tsaava (2018). The other two are investigated in the present paper. This allows to write a necessary and sufficient condition for the Fredholmness of the MIND BVP and to indicate a large set of the space parameters s > 1/p and 1 < p < ∞ for which the initial BVP is uniquely solvable in the nonclassical setting. As a consequence, we prove that the MIND BVP has a unique solution in the classical weak setting H1(C) for arbitrary complex values of the nonzero constant in the impedance condition. 1. Formulation of the problem. Let S ⊂ R be some smooth, closed, orientable surface, bordering a compact inner Ω and outer Ω− := R Ω+ domains. By C we denote a subsurface of S, which has two faces C− and C and inherits the orientation from S: C 2010 AMS Mathematics subject classification. Primary 35J57; Secondary 45E10, 47B35.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44918579","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: 2

Raising the regularity of generalized Abel equations in fractional Sobolev spaces with homogeneous boundary conditions 齐次边界条件下分数阶Sobolev空间中广义Abel方程正则性的提高

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-06-12 DOI: 10.1216/jie.2021.33.327

Yulong Li

{"title":"Raising the regularity of generalized Abel equations in fractional Sobolev spaces with homogeneous boundary conditions","authors":"Yulong Li","doi":"10.1216/jie.2021.33.327","DOIUrl":"https://doi.org/10.1216/jie.2021.33.327","url":null,"abstract":"The generalized (or coupled) Abel equations on the bounded interval have been well investigated in H$ddot{text{o}}$lderian spaces that admit integrable singularities at the endpoints and relatively inadequate in other functional spaces. In recent years, such operators have appeared in BVPs of fractional-order differential equations such as fractional diffusion equations that are usually studied in the frame of fractional Sobolev spaces for weak solution and numerical approximation; and their analysis plays the key role during the process of converting weak solutions to the true solutions. This article develops the mapping properties of generalized Abel operators $alpha {_aD_x^{-s}}+beta {_xD_b^{-s}}$ in fractional Sobolev spaces, where $0<alpha,beta$, $alpha+beta=1$, $ 0<s<1$ and $ {_aD_x^{-s}}$, $ {_xD_b^{-s}}$ are fractional Riemann-Liouville integrals. It is mainly concerned with the regularity property of $(alpha {_aD_x^{-s}}+beta {_xD_b^{-s}})u=f$ by taking into account homogeneous boundary conditions. Namely, we investigate the regularity behavior of $u(x)$ while letting $f(x)$ become smoother and imposing homogeneous boundary restrictions $u(a)=u(b)=0$.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45547035","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: 3

Polyconvolution of Hartley integral transforms $H_2$ and integral equations Hartley积分变换$H_2$与积分方程的多重卷积

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-06-01 DOI: 10.1216/jie.2020.32.171

N. M. Khoa, T. V. Thắng

引用次数: 1

On a class of noncompact weakly singular Volterra integral equations: theory and application to fractional differential equations with variable coefficient 一类非紧弱奇异Volterra积分方程:变系数分数阶微分方程的理论与应用

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-06-01 DOI: 10.1216/jie.2020.32.193

M. Toranj-Simin, M. Hadizadeh

引用次数: 0

Traveling wave solutions for a SEIR epidemic model in combination with random dispersal and nonlocal dispersal 随机扩散与非局部扩散相结合的SEIR流行病模型的行波解

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-06-01 DOI: 10.1216/jie.2020.32.213

Xin Wu, R. Yuan, Baochuan Tian

引用次数: 2

Square-mean almost automorphic solution of a stochastic cellular neural network on time scales 时间尺度上随机细胞神经网络的均方概自同构解

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-06-01 DOI: 10.1216/jie.2020.32.151

Soniya Dhama, Syed Abbas

引用次数: 5

Existence results for neutral integro-differential equations with nonlocal conditions 具有非局部条件的中立型积分微分方程的存在性结果

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-06-01 DOI: 10.1216/jie.2020.32.239

Jianbo Zhu, Xianlong Fu

引用次数: 6

Valuation of non-recourse stock loan using an integral equation approach 用积分方程法评估无追索权股票贷款

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-06-01 DOI: 10.1216/jie.2020.32.181

Nhat Le, M. Ngo

引用次数: 0

An optimized FD extrapolated scheme based on POD for the 2D integro-differential equation of parabolic type 基于POD的二维抛物型积分微分方程FD外推优化方案

IF 0.8 4区数学

Journal of Integral Equations and Applications Pub Date : 2020-03-01 DOI: 10.1216/jie.2020.32.35

Zhendong Luo

引用次数: 3