Title

Focusing Solutions Of Porous Medium Equations With Reaction

Keywords

Cauchy problem; Focusing self-similar solutions; Porous medium equation of reaction

Abstract

In this paper we study the existence of focusing solution to a class of porous medium equations taking the form ut=Δum+F(x,u,∇u), where m>1. Focusing solution has the property that its initial distribution is in the exterior of a finite domain. That is, there is a hole in the support of initial value, and in finite time T the hole disappears. We show there exists a focusing solution for a number of important models in physics and biology. Such solution is an example of a self-similar solution of the second kind. That is, the similarity variables cannot be determined a priori from dimensional consideration. Furthermore, it serves the purpose of supplying concrete bounds for the optimal regularity of general solutions of the equation. The P-Laplacian counterpart of this equation is also studied. © 2005 Elsevier Ltd. All rights reserved.

Publication Date

9-15-2005

Publication Title

Nonlinear Analysis, Theory, Methods and Applications

Volume

62

Issue

7

Number of Pages

1207-1224

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.na.2005.04.026

Socpus ID

22344440507 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/22344440507

This document is currently not available here.

Share

COinS