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

Ran Duan, Mina Jiang and Yinghui Zhang

Advances in Mathematical Physics, 2020, vol. 2020, 1-17

Abstract:

In this paper, we consider the asymptotic behavior of solutions to the - system with time-dependent damping on the half-line , with the Dirichlet boundary condition , in particular, including the constant and nonconstant coefficient damping. The initial data have the constant state at . We prove that the solutions time-asymptotically converge to as tends to infinity. Compared with previous results about the - system with constant coefficient damping, we obtain a general result when the initial perturbation belongs to . Our proof is based on the time-weighted energy method.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:3060867

DOI: 10.1155/2020/3060867

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