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Mathematische Annalen

, Volume 372, Issue 3–4, pp 1459–1479 | Cite as

When is the energy of the 1D damped Klein-Gordon equation decaying?

  • Satbir Malhi
  • Milena Stanislavova
Article
  • 61 Downloads

Abstract

We study time decay of the energy for the one dimensional damped Klein-Gordon equation. We give an explicit necessary and sufficient condition on the continuous damping function \(\gamma \ge 0\) for which the energy
$$\begin{aligned} E(t)=\int _{-\infty }^\infty |u_x|^2+|u|^2+ |u_t|^2 dx \end{aligned}$$
decays, whenever \((u(0), u_t(0))\in H^2(\mathbb R)\times H^1(\mathbb R)\).

Mathematics Subject Classification

35B35 35B40 35G30 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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