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June 2021 Optimal leading term of solutions to wave equations with strong damping terms
Hironori MICHIHISA
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Hokkaido Math. J. 50(2): 165-186 (June 2021). DOI: 10.14492/hokmj/2018-920

Abstract

We analyze the asymptotic behavior of solutions to wave equations with strong damping terms in $\textbf{R}^n$ $(n\ge1)$, $$ u_{tt}-\Delta u-\Delta u_t=0, \qquad u(0,x)=u_0(x), \quad u_t(0,x)=u_1(x). $$ If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the Fourier space are obtained, which implies the optimality of expanding methods and some estimates proposed in [13] and in this paper.

Acknowledgment

The author would like to thank Professor Ryo Ikehata for fruitful discussions and warm encouragement. The author is also grateful to the referees for careful reading and useful suggestions.

Citation

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Hironori MICHIHISA. "Optimal leading term of solutions to wave equations with strong damping terms." Hokkaido Math. J. 50 (2) 165 - 186, June 2021. https://doi.org/10.14492/hokmj/2018-920

Information

Received: 23 October 2018; Revised: 25 March 2019; Published: June 2021
First available in Project Euclid: 27 August 2021

Digital Object Identifier: 10.14492/hokmj/2018-920

Subjects:
Primary: 35B40, 35L25, 35L30

Rights: Copyright c 2021 Hokkaido University, Department of Mathematics

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Vol.50 • No. 2 • June 2021
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