Reverse norms and L∞ exponential decay for a class of degenerate evolution systems arising in kinetic theory

We consider the question of exponential decay to equilibrium of solutions of an abstract class of degenerate evolution equations on a Hilbert space modeling the steady Boltzmann and other kinetic equations. Specifically, we provide conditions suitable for construction of a stable manifold in a parti...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-07, Vol.475 (1), p.190-202
Main Authors: Pogan, Alin, Zumbrun, Kevin
Format: Article
Language:English
Subjects:
Boltzmann equation
Degenerate evolution equation
Stable manifold
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Summary:We consider the question of exponential decay to equilibrium of solutions of an abstract class of degenerate evolution equations on a Hilbert space modeling the steady Boltzmann and other kinetic equations. Specifically, we provide conditions suitable for construction of a stable manifold in a particular “reverse L∞” norm and examine when these do and do not hold.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.02.030