Part of the Trends in Mathematics book series (TM)
The Interplay Between Time-dependent Speed of Propagation and Dissipation in Wave Models
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
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 \(a\equiv1\)
KeywordsWave models damping term WKB analysis asymptotic profile scattering
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© Springer International Publishing Switzerland 2014