Asymptotic profile of solutions for strongly damped Klein-Gordon equations

Abstract

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.

arXiv comment19 pages. arXiv admin note: text overlap with arXiv:1706.07174

References in corpus (2)

• Semi-linear structural damped waves
• Asymptotic profile of solutions for some wave equations with very strong structural damping

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