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...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.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.11141004,11201296,11071162 and 11231006)
文摘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.
