Asymptotic profile of solutions for the damped wave equation with a nonlinear convection term |
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Authors: | Masakazu Kato Yoshihiro Ueda |
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Institution: | 1. Muroran Institute of Technology, Muroran 050‐8585, Japan;2. Kobe University, Kobe 658‐0022, Japan |
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Abstract: | This paper is concerned with the large time behavior of solutions to the initial value problem for the damped wave equations with nonlinear convection in one‐dimensional whole space. In 2007, Ueda and Kawashima showed that the solution tends to a self similar solution of the Burgers equation. However, they did not mention that their decay estimate is optimal or not. Under this situation, the aim of this paper was to find out the sharp decay estimate by studying the second asymptotic profile of solutions. The explicit representation formula and the decay estimates of the solution for the linearized equation including the lower order term play crucial roles in our analysis. |
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Keywords: | hyperbolic relaxation system large time behavior optimal decay estimates self‐similar solution |
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