Asymptotic expansion of the L2-norm of a solution of the strongly damped wave equation in space dimension 1 and 2

Article type: Research Article

Authors: Barrera, Joseph^{a; *} | Volkmer, Hans^b

Affiliations: [a] Department of Mathematics & Computer Science, Converse College, Spartanburg, SC 29302, USA. E-mail: joseph.barrera@converse.edu | [b] Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA. E-mail: volkmer@uwm.edu

Correspondence: [*] Corresponding author. E-mail: joseph.barrera@converse.edu.

Abstract: In previous work the authors found the asymptotic expansion of the L2-norm of the solution u(t,x) of the strongly damped wave equation utt−Δut−Δu=0 and also of the L2-norm of the difference between u(t,x) and its asymptotic approximation ν(t,x). This was done in space dimension N⩾3. In the present work results are extended to the exceptional cases N=1 and N=2. This extension is achieved by deriving new lemmas on the asymptotic expansion of some parameter dependent integrals.

Keywords: Asymptotic analysis, asymptotic expansion of L²-norm, wave equation, strong damping, Fourier analysis, weighted L₁ initial data

DOI: 10.3233/ASY-201606

Journal: Asymptotic Analysis, vol. 121, no. 3-4, pp. 367-399, 2021