Boundedness of global solutions for a heat equation with exponential gradient source
type: Item
instance of: scholarly article
title: Boundedness of global solutions for a heat equation with exponential gradient source
zbMATH Open document ID: 1254.35122
DOI: 10.1155/2012/398049
author: Zhengce Zhang
author: Yanyan Li
published in: Abstract and Applied Analysis
publication date: 2012-01-05T00:00:00Z
review text: Summary: We consider a one-dimensional semilinear parabolic equation with exponential gradient source and provide a complete classification of large time behavior of the classical solutions: either the space derivative of the solution blows up in finite time with the solution itself remaining bounded, or the solution is global and converges in \(C^1\) norm to the unique steady state. The main difficulty is to prove \(C^1\) boundedness of all global solutions. To do so, we explicitly compute a nontrivial Lyapunov's functional by carrying out the method of Zelenyak.
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 5994548
zbMATH Keywords: one space dimension
zbMATH Keywords: large time behavior
zbMATH Keywords: Lyapunov's functional
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/398049
OpenAlex ID: W2018653659
Wikidata QID: Q58696516
cites work: Dynamic Scaling of Growing Interfaces
cites work: Q5640108
cites work: Rate estimates of gradient blowup for a heat equation with exponential nonlinearity
cites work: Q5696831
description: scientific article; zbMATH DE number 5994548