Existence of infinitely many solutions for the one-dimensional Perona-Malik model

被引：46

作者：

Zhang, KW ^{[1
]}

机构：

[1] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2006年 / 26卷 / 02期

关键词：

Perona-Malik model; one-dimensional; infinitely many solutions; differential inclusion; relaxation property;

D O I：

10.1007/s00526-005-0363-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential inclusion problem.

引用

页码：171 / 199

页数：29

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