Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations
type: Item
instance of: scholarly article
title: Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations
zbMATH Open document ID: 1233.35022
author: Jing Li
author: Jingxue Yin
author: Chunhua Jin
published in: Central European Journal of Mathematics
publication date: 2011-12-12T00:00:00Z
review text: The Cauchy problem is investigated: \[ \begin{cases} u_t=u^q|\Delta u|^{m-1}\Delta u+u^p,\quad x\in \mathbb R^n, t>0,\\ u(x, 0)=u_0(x),\quad x\in \mathbb R^n, \end{cases} \tag{1} \] where \(q\geq 1\), \(m\geq 1\), \(p>0\), and \(u_0\) is nonnegative and appropriately smooth. The authors give conditions for the initial data \(u_0\) and for the parameters \(p\), \(q\) and \(m\) for local and global existence of generalized solutions of (1), for existence and uniqueness of the limit solutions of the Cauchy problem (1), for blow-up in finite time of the nontrivial solutions of (1), and for global existence of the limit solution of the considered problem (1).
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 5987918
zbMATH Keywords: limit solutions
zbMATH Keywords: nontrivial solutions
reviewed by: Svetlin Georgiev
MaRDI profile type: Publication
full work available at URL: s11533-011-0093-0
OpenAlex ID: W2131104344
cites work: Persistence and extinction in single-species reaction-diffusion models
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cites work: A stable manifold theorem for the curve shortening equation
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cites work: Blow-up for quasilinear heat equations with critical Fujita's exponents
cites work: A general approach to critical Fujita exponents in nonlinear parabolic problems
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cites work: On the regularity theory of fully nonlinear parabolic equations
cites work: A critical exponent in a degenerate parabolic equation
cites work: Classical solutions for a class of fully nonlinear degenerate parabolic equations
DOI: 10.2478/S11533-011-0093-0
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description: scientific article; zbMATH DE number 5987918