Boundary Effect on Asymptotic Behavior of Solutions to the p‐System with Time‐Dependent Damping

Ran Duan, Mina Jiang and Yinghui Zhang

Advances in Mathematical Physics, 2020, vol. 2020, issue 1

Abstract: In this paper, we consider the asymptotic behavior of solutions to the p‐system with time‐dependent damping on the half‐line R+=0,+∞, vt − ux = 0, ut + p(v)x = −(α/(1 + t)λ)u with the Dirichlet boundary condition u|x=0 = 0, in particular, including the constant and nonconstant coefficient damping. The initial data (v0, u0)(x) have the constant state (v+, u+) at x = +∞. We prove that the solutions time‐asymptotically converge to (v+, 0) as t tends to infinity. Compared with previous results about the p‐system with constant coefficient damping, we obtain a general result when the initial perturbation belongs to H3R+×H2R+. Our proof is based on the time‐weighted energy method.

Date: 2020
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https://doi.org/10.1155/2020/3060867

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:3060867

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