Differential and Integral Equations

Exponential decay for waves with indefinite memory dissipation

Bianca Morelli Rodolfo Calsavara and Higidio Portillo Oquendo

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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.

Article information

Source
Differential Integral Equations, Volume 30, Number 11/12 (2017), 975-988.

Dates
First available in Project Euclid: 1 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1504231282

Mathematical Reviews number (MathSciNet)
MR3693994

Zentralblatt MATH identifier
06819587

Subjects
Primary: 35B40: Asymptotic behavior of solutions 45D05: Volterra integral equations [See also 34A12] 74D99: None of the above, but in this section

Citation

Oquendo, Higidio Portillo; Calsavara, Bianca Morelli Rodolfo. Exponential decay for waves with indefinite memory dissipation. Differential Integral Equations 30 (2017), no. 11/12, 975--988. https://projecteuclid.org/euclid.die/1504231282


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