Asymptotic profile of solutions for strongly damped Klein-Gordon equations

We consider the Cauchy problem in the whole space for strongly damped Klein-Gordon equations. We derive asymptotic profles of solutions with weighted initial data by a simple method introduced by R. Ikehata. The obtained results show that the wave effect will be weak because of the mass term, especially in the low dimensional case (n = 1,2) as compared with the strongly damped wave equations without mass term (m = 0), so the most interesting topic in this paper is the n = 1,2 cases.