Radial weak solutions for the Perona-Malik equation as a differential inclusion
Analysis of PDEs
2013-10-01 v2
Abstract
The Perona-Malik equation is an ill-posed forward-backward parabolic equation with major application in image processing. In this paper we study the Perona-Malik type equation and show that, in all dimensions, there exist infinitely many radial weak solutions to the homogeneous Neumann boundary problem for any smooth nonconstant radially symmetric initial data. Our approach is to reformulate the -dimensional equation into a one-dimensional equation, to convert the one-dimensional problem into a differential inclusion problem, and to apply a Baire's category method to generate infinitely many solutions.
Keywords
Cite
@article{arxiv.1309.6646,
title = {Radial weak solutions for the Perona-Malik equation as a differential inclusion},
author = {Seonghak Kim and Baisheng Yan},
journal= {arXiv preprint arXiv:1309.6646},
year = {2013}
}
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41 pages