A remark on the global solvability of the Cauchy problem for quasilinear parabolic equations
type: Item
instance of: scholarly article
title: A remark on the global solvability of the Cauchy problem for quasilinear parabolic equations
zbMATH Open document ID: 0983.35057
author: A. S. Tersenov
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-12-04T00:00:00Z
reviewed by: Vladimir N. Grebenev
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1655650
zbMATH Keywords: unbounded growth of the nonlinearity
zbMATH Keywords: sufficient condition
MaRDI profile type: Publication
OpenAlex ID: W2017757812
cites work: Q5548525
cites work: FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
cites work: Q5731983
cites work: Derivative blow-up and beyond for quasilinear parabolic equations
cites work: Behavior of solutions to nonlinear parabolic equations at large time
cites work: Interior gradient blow-up in a semilinear parabolic equation
cites work: Q3360590
cites work: Interior derivative blow-up for quasilinear parabolic equations
cites work: QUASI-LINEAR SECOND-ORDER PARABOLIC EQUATIONS WITH MANY INDEPENDENT VARIABLES
cites work: Examples of parabolic problems with blowing-up derivatives
cites work: On solvability of some boundary value problems for a class of quasilinear parabolic equations
cites work: Q3901865
DOI: 10.1006/JMAA.2001.7434
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review text: The present article is devoted to studying the global solvability of the Cauchy problem for the quasilinear parabolic equation NEWLINE\[NEWLINE\begin{gathered} u_t = a(t,x,u,u_x)u_{xx} + f(t,x,u,u_x)\quad\text{in } \Pi_T (0,T)\times \mathbb{R}, \\ u(x,0) = u_0(x)\quad\text{for } x\in \mathbb{R}. \end{gathered}NEWLINE\]NEWLINE The main aim of the article under review is to expose a new (weaker) sufficient condition which guarantees the global solvability of the Cauchy problem. The author investigates the case of the arbitrary order of growth of the function \(f(t,x,u,p)\) with respect to \(p\) when \(|p|\to\infty\).
description: scientific article; zbMATH DE number 1655650