Well-posedness and long time behavior for a general class of Moore–Gibson–Thompson equations with a memory

We consider the well-posedness and the long time behavior of the Moore– Gibson–Thompson equation with memory in the critical case. We first find general sufficient conditions that guarantee a (optimal) polynomial decay of the system. Then by comparing the behavior of the resolvent of the Moore–Gibso...

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Bibliographic Details
Published inPortugaliae mathematica Vol. 78; no. 3; pp. 391 - 422
Main Authors Nicaise, Serge, Bounadja, Hizia
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 17.01.2022
Subjects
Analysis of PDEs
Kernel functions
Mathematical research
Mathematics
Polynomials
Wave equation
France
Mathematics Subject Classification: 35B37
74D05
93D15
wave equation
Mathematics Subject Classification: 35B37 35L55 74D05 93D15 93D20 Moore-Gibson-Thompson equation memory kernel polynomial stability wave equation
93D20 Moore-Gibson-Thompson equation
polynomial stability
35L55
memory kernel
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ISSN0032-5155
1662-2758
DOI10.4171/pm/2074

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Summary:We consider the well-posedness and the long time behavior of the Moore– Gibson–Thompson equation with memory in the critical case. We first find general sufficient conditions that guarantee a (optimal) polynomial decay of the system. Then by comparing the behavior of the resolvent of the Moore–Gibson–Thompson system with the one of the resolvent of the wave equation with a frictional interior damping, we furnish a stronger polynomial decay of the solution.
ISSN:0032-5155
1662-2758
DOI:10.4171/pm/2074