On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources
type: Item
instance of: scholarly article
title: On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources
zbMATH Open document ID: 1183.35184
author: Junning Zhao
author: Tingting Zheng
published in: Science in China. Series A
publication date: 2009-12-07T00:00:00Z
review text: The existence of solutions to the problem \[ u_t= \text{div}(|\nabla u^m|^{p-2}\nabla u^m)+ {u^q\over(1+|x|)^\alpha},\qquad u(x,0)= u_0(x) \] is considered in \(\mathbb{R}^n\times (0,T]\). Here \(p> 2\), \(m> 1\), \(q> 1\) but \(\alpha\) is arbitrary. The results include some quantitative estimates.
reviewed by: Peter Lindqvist
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 5643343
zbMATH Keywords: evolutionary equation
zbMATH Keywords: existence of solutions
zbMATH Keywords: degenerate equations
MaRDI profile type: Publication
full work available at URL: s11425-007-0168-3
OpenAlex ID: W2035356378
cites work: Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
cites work: Q4007944
cites work: On the Cauchy problem and initial traces for the evolution \(p\)-Laplacian equations with strongly nonlinear sources
cites work: Cauchy problem and initial trace for a doubly degenerate parabolic equation with strongly nonlinear sources
cites work: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
DOI: 10.1007/S11425-007-0168-3
description: scientific article; zbMATH DE number 5643343