摘要
In this paper,we consider the large perturbation around the viscous shock of the scalar conservation law with viscosity in one dimension case.We divide the time region into t≤T0 and t>T0 for a fixed constant T0 when applying energy method.Since T0 is fixed,the case t≤T0 is easy to deal with and when t>T0,from the decaying property of the solution,there is a priori estimate for the solution.Thus we can succeed to control the nonlinear term and get the pointwise estimate for the perturbation by the weighted energy method.
In this paper, we consider the large perturbation around the viscous shock of the scalar conservation law with viscosity in one dimension case. We divide the time region into t ≤T0 and t 〉 To for a fixed constant To when applying energy method. Since To is fixed, the case t ≤ To is easy to deal with and when t 〉 To, from the decaying property of the solution, there is a priori estimate for the solution. Thus we can succeed to control the nonlinear term and get the pointwise estimate for the perturbation by the weighted energy method.
基金
supported by National Natural Science Foundation of China (Grant Nos.11141004,11201296,11071162 and 11231006)
关键词
守恒定律
大扰动
衰减率
粘性
先验估计
逐点估计
非线性项
tgt
viscous conservation law
one dimension
shock profile
large initial data
weighted energy esti- mate
pointwise estimate
