The pressure equation in the fast diffusion range
type: Item
instance of: scholarly article
title: The pressure equation in the fast diffusion range
zbMATH Open document ID: 1073.35128
DOI: 10.4171/RMI/373
author: E. Chasseigne
author: Juan Luis Vázquez
published in: Revista Matemática Iberoamericana
publication date: 2004-10-25T00:00:00Z
full work available at URL: https://eudml.org/doc/39591
review text: The authors study the equation \[ v_t=v\Delta v - \gamma| \nabla v| ^2\qquad \text{in } {\mathbb R}^N\times (0,\infty), \] which is an example of a fully nonlinear parabolic equation in non-divergence form. The equation is not well-understood when \(\gamma>0\). In this paper, the authors concentrate on the range \(\gamma>N/2\). They show that the Cauchy problem is well-posed with arbitrarily large initial data, understood in the sense of Borel \(p\)-trace where \(p=-\gamma<0\), and solutions are classical. The authors also point out why classical approaches do not work.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 2109870
zbMATH Keywords: pressure equation
zbMATH Keywords: fast diffusion
zbMATH Keywords: well-posedness
zbMATH Keywords: non-divergence form
reviewed by: Peter Y. H. Pang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2109870