Existence and uniqueness of weak solutions for nonlocal parabolic problems via the Galerkin method

被引：7

作者：

Yangari, Miguel ^{[1
,2
]}

机构：

[1] Escuela Politec Nacl, Res Ctr Math Modelling MODEMAT, Ladron de Guevara E11-253,POB 17-01-2759, Quito, Ecuador

[2] Escuela Politec Nacl, Dept Matemat, Ladron de Guevara E11-253,POB 17-01-2759, Quito, Ecuador

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 463卷 / 02期

关键词：

Nonlocal operator; Nonlocal vector calculus; Weak solution; Galerkin method; APPROXIMATION; EQUATIONS;

D O I：

10.1016/j.jmaa.2018.03.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fractional differential equations are becoming increasingly popular as a modeling tool to describe a wide range of non-classical phenomena with spatial heterogeneities throughout the applied science and engineering. A recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal operators which include fractional Laplacian on bounded domains in R-n. We develop the Galerkin method to prove existence and uniqueness of weak solutions to nonlocal parabolic problems. Moreover, we study the existence of orthonormal basis of eigenvectors associated to these nonlocal operators. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：910 / 921

页数：12

共 23 条

[1] A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian [J].