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Abstract

We study the Cauchy problem for a damped wave equation. Our main result is the $(N + 1)$ th order approximation of solutions by the solution of the corresponding parabolic equation for arbitrary $N \in N$ in the $L^{p}$ framework. This means that our results can be applied to nonlinear damped wave equations.

Keywords

damped wave equation asymptotic profile the Cauchy problem higher-order expansion of solution

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Higher-order expansion of solutions for a damped wave equation

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