TY - JOUR
T1 - Decay Rate Toward the Traveling Wave for Scalar Viscous Conservation Law
AU - Huang , Feimin
AU - Xu , Lingda
JO - Communications in Mathematical Analysis and Applications
VL - 3
SP - 395
EP - 409
PY - 2022
DA - 2022/06
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmaa/20662.html
KW - Viscous conservation law, shock wave, decay rate.
AB - <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>