On wave equation: review and recent results

The aim of this paper is to give an overview of results related to nonlinear wave equations during the last half century. In this regard, we present results concerning existence, decay and blow up for classical nonlinear equations. After that, we discuss briefly some important results of the variabl...

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Bibliographic Details
Published inArabian Journal of Mathematics Vol. 7; no. 2; pp. 113 - 145
Main Authors Messaoudi, Salim A., Talahmeh, Ala A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Springer
Springer Nature B.V
Subjects
Decay
Existence theorems
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
Sobolev space
Sobolev spaces
Wave equations
35L05
35L70
35B35
35B44
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Summary:The aim of this paper is to give an overview of results related to nonlinear wave equations during the last half century. In this regard, we present results concerning existence, decay and blow up for classical nonlinear equations. After that, we discuss briefly some important results of the variable-exponent Lebesgue and Sobolev spaces. Results related to nonexistence and blow up for wave equations with non-standard nonlinearities (nonlinearities involving variable exponents) are given in more detail. Finally, we present some recent decay and blow up results together with their proofs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-017-0190-4