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

Author

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  • Ran Duan
  • Mina Jiang
  • Yinghui Zhang

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.

Suggested Citation

  • Ran Duan & Mina Jiang & Yinghui Zhang, 2020. "Boundary Effect on Asymptotic Behavior of Solutions to the - System with Time-Dependent Damping," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-17, January.
  • Handle: RePEc:hin:jnlamp:3060867
    DOI: 10.1155/2020/3060867
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