The local strong and weak solutions for a generalized pseudoparabolic equation
type: Item
instance of: scholarly article
title: The local strong and weak solutions for a generalized pseudoparabolic equation
zbMATH Open document ID: 1246.35113
DOI: 10.1155/2012/568404
author: Nan Li
published in: Abstract and Applied Analysis
publication date: 2012-07-18T00:00:00Z
review text: Summary: The Cauchy problem for a nonlinear generalized pseudoparabolic equation is investigated. The well-posedness of local strong solutions for the problem is established in the Sobolev space \(C([0, T); H^s(\mathbb R)) \bigcap C^1([0, T); H^{s-1}(\mathbb R))\) with \(s > 3/2\), while the existence of local weak solutions is proved in the space \(H^s(\mathbb R)\) with \(1 \leq s \leq 3/2\). Further, under certain assumptions of the nonlinear terms in the equation, it is shown that there exists a unique global strong solution to the problem in the space \(C([0, \infty); H^s(\mathbb R)) \bigcap C^1([0, \infty); H^{s-1}(\mathbb R))\) with \(s \geq 2\).
Mathematics Subject Classification ID: 35K70
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 6058130
zbMATH Keywords: well-posedness
zbMATH Keywords: global strong solution
Wikidata QID: Q58695543
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/568404
OpenAlex ID: W2116122008
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description: scientific article; zbMATH DE number 6058130