Diffusion phenomena for partially dissipative hyperbolic systems

Details Diffusion phenomena for partially dissipative hyperbolic systems Diffusion phenomena for partially dissipative hyperbolic systems

2011-10-04

arxiv.org/abs/1110.0797v2

Mathematics

Analysis of PDEs

7 pages, some minor corrections

Scientific paper

In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural) conditions solutions to a partially dissipative hyperbolic system are asymptotically equivalent to solutions of a corresponding parabolic equation. The approach is based on an elliptic WKB analysis for small frequencies in combination with exponential stability for large frequencies due to results of Beauchard and Zuazua and arguments of perturbation theory.

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