WEAK SOLUTION TO AN EVOLUTION PROBLEM WITH A NONLOCAL CONSTRAINT

被引：71

作者：

SHI, P

机构：

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1993年 / 24卷 / 01期

关键词：

NONLOCAL CONDITION; WEIGHTED SOBOLEV SPACE;

D O I：

10.1137/0524004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A parabolic problem is considered with a nonlocal constraint in place of one of the standard boundary conditions. Well-posedness of the problem is proved in a weighted, fractional Sobolev space with the problem data proposed in related weighted spaces. This comes as an intrinsic requirement of the problem. The proof uses an interpolation inequality for norms of fractional Sobolev spaces and is based on an interesting choice of the test function.

引用

页码：46 / 58

页数：13