Optimal decay rates for nonlinear Moore-Gibson-Thompson equation with memory and Neumann boundary

We consider the initial value problem of Moore-Gibson-Thompson equation with memory effect, being subject to the Neumann boundary condition. Here, the nonlinearity f is conservative and satisfies some polynomial growth conditions. Under the condition that $ g(t) $ g ( t ) decays exponentially, we ob...

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Bibliographic Details
Published inApplicable analysis Vol. 104; no. 2; pp. 293 - 313
Main Author Zhang, Hui
Format Journal Article
LanguageEnglish
Published Taylor & Francis 22.01.2025
Subjects
energy
memory effect
Moore-Gibson-Thompson equation
Neumann boundary
optimal decay
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Summary:We consider the initial value problem of Moore-Gibson-Thompson equation with memory effect, being subject to the Neumann boundary condition. Here, the nonlinearity f is conservative and satisfies some polynomial growth conditions. Under the condition that $ g(t) $ g ( t ) decays exponentially, we obtain the uniform polynomial decaying rate of energy and the solution. Moreover, we show this decay rate is optimal in the sense that there exists a class of solutions decaying exactly at this rate.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2024.2360506