Open AccessNonlinear stability of rarefaction waves for a hyperbolic system with Cattaneo's law
Author(s) -
Yinsong Bai,
Lin He,
Huijiang Zhao
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021049
Subject(s) - conservation law , norm (philosophy) , mathematics , scalar (mathematics) , physics , mathematical analysis , initial value problem , mathematical physics , perturbation (astronomy) , nonlinear system , law , geometry , quantum mechanics , political science
This paper is concerned with the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem and the initial-boundary value problem in the half space with impermeable wall boundary condition for a scalar conservation laws with an artificial heat flux satisfying Cattaneo's law. In our results, although the \begin{document}$ L^2\cap L^\infty- $\end{document} norm of the initial perturbation is assumed to be small, the \begin{document}$ H^1- $\end{document} norm of the first order derivative of the initial perturbation with respect to the spatial variable can indeed be large. Moreover the far fields of the artificial heat flux can be different. Our analysis is based on the \begin{document}$ L^2 $\end{document} energy method.