Year: 2022
Author: Feimin Huang, Lingda Xu
Communications in Mathematical Analysis and Applications, Vol. 1 (2022), Iss. 3 : pp. 395–409
Abstract
The time-decay rate toward the viscous shock wave for scalar viscous conservation law $$u_t+ f(u)_x =\mu u_{xx}$$ is obtained in this paper through an $L^p$ estimate and the area inequality in [1] provided that the initial perturbations are small, i.e., $||\Phi_0||_{H^2}≤ε,$ where $\Phi_0$ is the anti-derivative of the initial perturbation. It is noted that there is no additional weighted requirement on $\Phi_0,$ i.e., $\Phi_0(x)$ only belongs to $H^2 (R).$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-CMAA-20662
Communications in Mathematical Analysis and Applications, Vol. 1 (2022), Iss. 3 : pp. 395–409
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Viscous conservation law shock wave decay rate.