The Half Space Problem For P-System With Damping

In this paper,the author studies on the problem that the stability of the solution to the initial-boundary value problem for p-system with damping in half space.We will mainly introduce how to use the green's function method to get the point-wise estimates of the solution and how to apply A-C scheme to determine proper boundary conditions for initial-boundary value problems in the half space and to construct point-wise structures of the boundary data.Firstly,we linearize the nonlinear system at M ?(1,0)state and,then obtain the full boundary data by way of A-C scheme and write the solution by using Green's identity,so that we can ultimately achieve the estimate of the solution.Secondly,we obtain the pointwise estimates mainly based on the detailed analysis and micro-local analysis of the fundamental solution for the linear part,mainly fourier transform,spectrum decomposition,energy integral,to construct the fundamental solution to initial value problem;based on this,we gain the point-wise estimates of the Green's function.