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The Interplay Between Time-dependent Speed of Propagation and Dissipation in Wave Models

  • Tang Bao Ngoc BuiEmail author
  • Michael Reissig
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The aim of this paper is to understand the influence of the interplay between a time-dependent increasing speed of propagation and a timedependent coefficient in the dissipation on qualitative properties of solutions to the wave model
$$u_{tt}-a^2(t)\bigtriangleup\mathrm{u}+ b(t)u_t=0,\,u(0,x)=u_1(x),u_{t}(0,x)=u_{2}(x).$$
Our considerations are focused to energy estimates. The main difficulty is to find a good description of non-effective and effective dissipations depending on a given speed of propagation. The obtained energy estimates are optimal as special examples will show. At the end we will sketch very briefly how to get scattering and over-damping results. So, we propose a classification of different damping terms which is motivated by the thesis of J. Wirth for the case \(a\equiv1\)

Keywords

Wave models damping term WKB analysis asymptotic profile scattering 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute of Applied AnalysisTU Bergakademie FreibergFreibergGermany

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