Abstract
This paper is concerned with the asymptotic behavior of the solution of quasilinear hyperbolic equations with linear damping. The main novelty lies in the following observation: If we suitably choose the initial data of the corresponding parabolic equation, then the solution Psi = Psi(x, t) of the parabolic equation served as the new asymptotic profile satisfies parallel to(V - Psi, (V - Psi)(x), (V - Psi)(t))(t)parallel to(L)infinity = O(1)(t(-2), t(-5/2), t(-3)). The convergence rates of the new profile. are better than that obtained by H.-J. Zhao (2000, J. Differential Equations 167, 467-494), and we need none of the additional technical assumptions (H-1) and (H-2) therein. Therefore, we answer an open problem posed by Nishihara (1997, J. Differential Equations 133, 384-395).
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