@article{oai:kanazawa-u.repo.nii.ac.jp:00011105,
 author = {Hashimoto, Itsuko and Ueda, Yoshihiro},
 issue = {1},
 journal = {Osaka Journal of Mathematics},
 month = {Mar},
 note = {We study the asymptotic stability of nonlinear waves for damped wave equations with a convection term on the half line. In the case where the convection term satisfies the convex and sub-characteristic conditions, it is known by the work of Ueda [7] and Ueda-Nakamura-Kawashima [10] that the solution tends toward a stationary solution. In this paper, we prove that even for a quite wide class of the convection term, such a linear superposition of the stationary solution and the rarefaction wave is asymptotically stable. Moreover, in the case where the solution tends to the non-degenerate stationary wave, we derive that the time convergence rate is polynomially (resp. exponentially) fast if the initial perturbation decays polynomially (resp. exponentially) as x → ∞. Our proofs are based on a technical L 2 weighted energy method.},
 pages = {37--52},
 title = {Asymptotic behavior of solutions for damped wave equations with non-convex convection term on the half line},
 volume = {49},
 year = {2012}
}