This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointw...This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointwise decay of the perturbation and but also the high derivative of it. Stability in anyL(p≥1) norm is a direct consequence.展开更多
Cauchy problem of Cahn-Hilliard equation with inertial term in three-dimensional space is considered.Using delicate analysis of its Green function and its convolution with nonlinear term,pointwise decay rate is obtained.
基金the National Natural Science Foundation of China(10131050)
文摘This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointwise decay of the perturbation and but also the high derivative of it. Stability in anyL(p≥1) norm is a direct consequence.
基金Supported by the National Natural Science Foundation of China(11801137)。
文摘Cauchy problem of Cahn-Hilliard equation with inertial term in three-dimensional space is considered.Using delicate analysis of its Green function and its convolution with nonlinear term,pointwise decay rate is obtained.
