Well-posedness and blow-up of solutions for the p(l)-biharmonic wave equation with singular dissipation and variable-exponent logarithmic source

This research examines the well-posedness and blow-up phenomena associated with a p(l)-biharmonic wave equation characterized by singular dissipation and a variable-exponent logarithmic source term, subject to null Dirichlet boundary conditions. Utilizing contraction mapping principle and Faedo-Gale...

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Bibliographic Details
Published inJournal of pseudo-differential operators and applications Vol. 16; no. 1
Main Authors Shahrouzi, Mohammad, Boulaaras, Salah, Jan, Rashid
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.03.2025
Subjects
Biharmonic equations
Boundary conditions
Concavity
Differential equations
Dissipation
Galerkin method
Logarithms
Wave equations
Well posed problems
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Summary:This research examines the well-posedness and blow-up phenomena associated with a p(l)-biharmonic wave equation characterized by singular dissipation and a variable-exponent logarithmic source term, subject to null Dirichlet boundary conditions. Utilizing contraction mapping principle and Faedo-Galerkin method, the global and local well-posedness of the equation are established. Furthermore, the blow-up behavior, both in finite and infinite time, is demonstrated through the application of a modified concavity argument.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-025-00680-z