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

摘要

In previous work the authors found the asymptotic expansion of the L-2-norm of the solution u(t, x) of the strongly damped wave equation u(tt) - Delta u(t) - Delta u = 0 and also of the L-2-norm of the difference between u(t, x) and its asymptotic approximation v(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.