Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities
type: Item
instance of: scholarly article
title: Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities
zbMATH Open document ID: 1018.35048
author: E. Chasseigne
author: Juan Luis Vázquez
published in: Archive for Rational Mechanics and Analysis
publication date: 2003-03-13T00:00:00Z
review text: This paper deals with the extending of the existing theory of nonnegative solutions of the nonlinear evolution equation \[ u_t=\Delta (u^m),\;0< m<1, \] which serves as a mathematical model for the interplay of fast and slow propagation speeds in an evolution process of diffusive type. The goal of the authors is to formulate a theory of existence, uniqueness and continuous dependence of solutions with arbitrarily large data in a suitable class of large data in a suitable class of large solutions, as well as the inverse problem of assigning an initial trace to any given solution. The authors show that for the range \[ m_c<m<1,\;m_c= \max\left\{ {N-2\over N},0 \right\} \] three closely related problems can be solved in an optimal way. The authors emphasize the main novelty of their study, namely the existence of strong singularities which behave like permanent sources of radiation.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 1882090
zbMATH Keywords: existence, uniqueness and continuous dependence
zbMATH Keywords: fast and slow propagation speeds
zbMATH Keywords: strong singularities
zbMATH Keywords: permanent sources of radiation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s00205-002-0210-0
OpenAlex ID: W2050809524
DOI: 10.1007/S00205-002-0210-0
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description: scientific article; zbMATH DE number 1882090