Decay Rate Toward the Traveling Wave for Scalar Viscous Conservation Law

Decay Rate Toward the Traveling Wave for Scalar Viscous Conservation Law

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.

Author Details

Feimin Huang

Lingda Xu