| Abstract: | This paper presents new methods widely applicable to expand solutions for wave equations with damping terms such as Rosenau‐type equations. Some of them have the diffusion structure that appears strongly in the low‐frequency region, and some detailed analysis on diffusion waves is seen in this report. In the high‐frequency region, difficulties arising from the regularity‐loss type are overcome by a new discovery of suitable asymptotic profiles and expanding techniques of solutions even if regularity assumptions on the initial data are not imposed. It is also shown that stronger regularity assumptions on the initial data give better asymptotic estimates. |
