Abstract
This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous gases in the half space. We discuss the following two cases: (1) viscous conservation laws and (2) damped wave equations with nonlinear convection. In each case, we prove that the solution converges to the corresponding degenerate stationary wave at the rate t−α/4 as t → ∞, provided that the initial perturbation is in the weighted space \({L^2_\alpha=L^2({\mathbb R}_+;\,(1+x)^\alpha dx)}\) . This convergence rate t−α/4 is weaker than the one for the non-degenerate case and requires the restriction α α*(q) with another critical value α*(q). Our stability analysis is based on the space–time weighted energy method in which the spatial weight is chosen as a function of the degenerate stationary wave.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
