@Article{CMAA-1-3,
author = {Huang, Feimin and Xu, Lingda},
title = {Decay Rate Toward the Traveling Wave for Scalar Viscous Conservation Law},
journal = {Communications in Mathematical Analysis and Applications},
year = {2022},
volume = {1},
number = {3},
pages = {395--409},
abstract = {<p style="text-align: justify;">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 $H^2
(R).$</p>},
issn = {2790-1939},
doi = {https://doi.org/2022-CMAA-20662},
url = {https://global-sci.com/article/81435/decay-rate-toward-the-traveling-wave-for-scalar-viscous-conservation-law}
}