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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.

advances in mathematical physics

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