We consider the Cauchy problem in R n for strongly damped wave equations. We derive asymptotic profiles of these solutions with weighted L 1,1 (R n ) data by using a method introduced in [10].

No abstract

No abstract

SUMMARYWe present new decay estimates of solutions for the mixed problem of the equation vtt − vxx + vt = 0, which has the weighted initial data. Similar decay estimates are also derived to the Cauchy problem in R N for utt − u+ut = 0 with the weighted initial data. Finally, these decay estimates can be applied to the one dimensional critical exponent problem for a semilinear damped wave equation on the half line.

No abstract