Higher-order expansion of solutions for a damped wave equation

Article type: Research Article

Authors: Takeda, Hiroshi

Affiliations: Department of Intelligent Mechanical Engineering, Faculty of Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-Higashi, Higashi-ku, Fukuoka, 811-0295 Japan. Tel.: +81 92 606 4229; Fax: +81 92 606 0747; E-mail: h-takeda@fit.ac.jp

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∈N in the Lp 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

DOI: 10.3233/ASY-151295

Journal: Asymptotic Analysis, vol. 94, no. 1-2, pp. 1-31, 2015