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VOL. 64 | 2015 Diffusion phenomena for partially dissipative hyperbolic systems
Jens Wirth

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

Abstract

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.

Information

Published: 1 January 2015
First available in Project Euclid: 30 October 2018

zbMATH: 1347.35142
MathSciNet: MR3381216

Digital Object Identifier: 10.2969/aspm/06410303

Subjects:
Primary: 35L03
Secondary: 35B40, 35B45

Rights: Copyright © 2015 Mathematical Society of Japan

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