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.
We are interested in the Klein-Gordon-Zakharov system in R1+2,which is an important model in plasma physics with extensive mathematical studies.The system can be regarded as semilinear coupled wave and Klein-Gordon eq...We are interested in the Klein-Gordon-Zakharov system in R1+2,which is an important model in plasma physics with extensive mathematical studies.The system can be regarded as semilinear coupled wave and Klein-Gordon equations with nonlinearities violating the null conditions.Without the compactness assumptions on the initial data,we aim to establish the existence of small global solutions,and in addition,we want to illustrate the optimal pointwise decay of the solutions.Furthermore,we show that the Klein-Gordon part of the system enjoys linear scattering,while the wave part has uniformly bounded low-order energy.None of these goals is easy because of the slow pointwise decay nature of the linear wave and Klein-Gordon components in R1+2.We tackle the difficulties by carefully exploiting the properties of the wave and the Klein-Gordon components,and by relying on the ghost weight energy estimates to close higher order energy estimates.This appears to be the first pointwise decay result and the first scattering result for the Klein-Gordon-Zakharov system in R1+2 without compactness assumptions.展开更多
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.
文摘We are interested in the Klein-Gordon-Zakharov system in R1+2,which is an important model in plasma physics with extensive mathematical studies.The system can be regarded as semilinear coupled wave and Klein-Gordon equations with nonlinearities violating the null conditions.Without the compactness assumptions on the initial data,we aim to establish the existence of small global solutions,and in addition,we want to illustrate the optimal pointwise decay of the solutions.Furthermore,we show that the Klein-Gordon part of the system enjoys linear scattering,while the wave part has uniformly bounded low-order energy.None of these goals is easy because of the slow pointwise decay nature of the linear wave and Klein-Gordon components in R1+2.We tackle the difficulties by carefully exploiting the properties of the wave and the Klein-Gordon components,and by relying on the ghost weight energy estimates to close higher order energy estimates.This appears to be the first pointwise decay result and the first scattering result for the Klein-Gordon-Zakharov system in R1+2 without compactness assumptions.
