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November/December 2017 Exponential decay for waves with indefinite memory dissipation
Bianca Morelli Rodolfo Calsavara, Higidio Portillo Oquendo
Differential Integral Equations 30(11/12): 975-988 (November/December 2017).

Abstract

In this work, we deal with the following wave equation with localized dissipation given by a memory term $$ u_{tt} -u_{xx} + \partial_x \Big\{ a(x)\int_{0}^{t} g(t-s)u_{x}(x,s)ds \Big\}=0. $$ We consider that this dissipation is indefinite due to sign changes of the coefficient $a$ or by sign changes of the memory kernel $g$. The exponential decay of solutions is proved when the average of coefficient $a$ is positive and the memory kernel $g$ is small.

Citation

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Bianca Morelli Rodolfo Calsavara. Higidio Portillo Oquendo. "Exponential decay for waves with indefinite memory dissipation." Differential Integral Equations 30 (11/12) 975 - 988, November/December 2017.

Information

Published: November/December 2017
First available in Project Euclid: 1 September 2017

zbMATH: 06819587
MathSciNet: MR3693994

Subjects:
Primary: 35B40, 45D05, 74D99

Rights: Copyright © 2017 Khayyam Publishing, Inc.

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Vol.30 • No. 11/12 • November/December 2017
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