We consider the Cauchy problem in R n for strongly damped Klein-Gordon equations. We derive asymptotic profiles of solutions with weighted L 1,1 (R n ) initial data by a simple method introduced by the second author. Furthermore, from the obtained asymptotic profile, we get the optimal decay order of the L 2 -norm of solutions. The obtained results show that the wave effect will be relatively 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 to compare the difference.

Asymptotic profile of solutions for strongly damped Klein-Gordon equations

D'Abbicco M.;
2019

Abstract

We consider the Cauchy problem in R n for strongly damped Klein-Gordon equations. We derive asymptotic profiles of solutions with weighted L 1,1 (R n ) initial data by a simple method introduced by the second author. Furthermore, from the obtained asymptotic profile, we get the optimal decay order of the L 2 -norm of solutions. The obtained results show that the wave effect will be relatively 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 to compare the difference.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/238195
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