Energy asymptotics for the strongly damped Klein–Gordon equation

Haidar Mohamad ()
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Haidar Mohamad: Katholische Universität Eichstätt-Ingolstadt

Partial Differential Equations and Applications, 2022, vol. 3, issue 6, 1-12

Abstract: Abstract We consider the strongly damped Klein–Gordon equation for defocusing nonlinearity and we study the asymptotic behaviour of the energy for periodic solutions. We prove first the exponential decay to zero for zero mean solutions. Then, we characterize the limit of the energy, when the time tends to infinity, for solutions with small enough initial data and we finally prove that such limit is not necessary zero.

Keywords: Klein–Gordon equation; Strong and weak damping; Energy decay; 35Qxx (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00207-x

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