Large Time Asymptotics for Partially Dissipative Hyperbolic Systems
Beauchard K, Zuazua E (2011)
Publication Type: Journal article
Publication year: 2011
Journal
Book Volume: 199
Pages Range: 177-227
Journal Issue: 1
DOI: 10.1007/s00205-010-0321-y
Abstract
This work is concerned with (n-component) hyperbolic systems of balance laws in m space dimensions. First, we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t -> infinity. Using the Fourier transform, we examine the role that control theoretical tools, such as the classical Kalman rank condition, play. We build Lyapunov functionals allowing us to establish explicit decay rates depending on the frequency variable. In this way we extend the previous analysis by Shizuta and Kawashima under the so-called algebraic condition (SK). In particular, we show the existence of systems exhibiting more complex behavior than the one that the (SK) condition allows. We also discuss links between this analysis and previous literature in the context of damped wave equations, hypoellipticity and hypocoercivity. To conclude, we analyze the existence of global solutions around constant equilibria for nonlinear systems of balance laws. Our analysis of the linear case allows proving existence results in situations that the previously existing theory does not cover.
Authors with CRIS profile
Involved external institutions
École Polytechnique - Université Paris-Saclay
France (FR)
Basque Center of Applied Mathematics (BCAM)
Spain (ES)
France (FR)
Basque Center of Applied Mathematics (BCAM)
Spain (ES)
How to cite
APA:
Beauchard, K., & Zuazua, E. (2011). Large Time Asymptotics for Partially Dissipative Hyperbolic Systems. Archive for Rational Mechanics and Analysis, 199(1), 177-227. https://dx.doi.org/10.1007/s00205-010-0321-y
MLA:
Beauchard, Karine, and Enrique Zuazua. "Large Time Asymptotics for Partially Dissipative Hyperbolic Systems." Archive for Rational Mechanics and Analysis 199.1 (2011): 177-227.
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