Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type
type: Item
instance of: scholarly article
title: Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type
zbMATH Open document ID: 0891.35062
author: Sang Ro Park
author: James Serrin
author: Howard A. Levine
published in: Journal of Differential Equations
publication date: 1998-07-01T00:00:00Z
review text: The authors study global existence and nonexistence of solutions of abstract quasilinear evolution problems involving potential operators. Using energy methods, they show nonexistence of global solutions provided the energy of the initial function is negative (or \(\ll0\)). The global existence result is based on suitable structure conditions on the corresponding potentials. The abstract theory is illustrated by examples of the type \(|u_t|^{m-2}u_t-a\nabla\cdot(|\nabla u|^{q-2}\nabla u)=|u|^{p-2}u\).
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1130548
zbMATH Keywords: blow-up
zbMATH Keywords: abstract quasi-linear evolution problems
zbMATH Keywords: potential operators
zbMATH Keywords: energy methods
reviewed by: Pavol Quittner
MaRDI profile type: Publication
full work available at URL: jdeq.1997.3362
OpenAlex ID: W2026085953
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DOI: 10.1006/JDEQ.1997.3362
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description: scientific article; zbMATH DE number 1130548