Differential and Integral Equations

Fast energy decay for wave equations with variable damping coefficients in the $1$-D half line

Ryo Ikehata and Takeshi Komatsu

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Abstract

We derive fast decay estimates of the total energy for wave equations with localized variable damping coefficients, which are dealt with in the one dimensional half line $(0,\infty)$. The variable damping coefficient vanishes near the boundary $x = 0$, and is effective critically near spatial infinity $x = \infty$.

Article information

Source
Differential Integral Equations Volume 29, Number 5/6 (2016), 421-440.

Dates
First available in Project Euclid: 9 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1457536885

Mathematical Reviews number (MathSciNet)
MR3471967

Zentralblatt MATH identifier
06562183

Subjects
Primary: 35L20: Initial-boundary value problems for second-order hyperbolic equations 35L05: Wave equation 5B33 35B40: Asymptotic behavior of solutions

Citation

Ikehata, Ryo; Komatsu, Takeshi. Fast energy decay for wave equations with variable damping coefficients in the $1$-D half line. Differential Integral Equations 29 (2016), no. 5/6, 421--440. https://projecteuclid.org/euclid.die/1457536885.


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