Stability And Convergence Rates Of Boundary Layer Solution For Damped Wave Equation In The Two-Dimensional Half Space

The damped wave equations are of great theoretical significance and research value.It can describe a uniform rod micro vibration in the longitudinal direction and other issues. About the Cauchy problem of the damped wave equation, because of the boundary conditions, boundary layer solution can also be used to describe the large time behavior of their solution.Under the premise of a nonlinear convection term, this paper is related to the initial-boundary value problem in the two-dimensional half space. In the non-degenerate condition that is f?1(u+) < 0 and without considering strict convexity of f1(u) and small property of the wave intensity ? = |u+-ub|, it mainly describes the existence, uniqueness,asymptotics of stationary wave and the algebraic convergence when the solution of the initial-boundary value problem tends to stationary wave.The first chapter, describes the research status of the damped wave equations and its Cauchy problem. It also introduces the main idea of this paper.The second chapter, by the method of solving ordinary differential equations and the use of image compression principle we obtain the existence and uniqueness of the stationary wave ?(x1). Monotonicity and asymptotics are obtained by integrating the operation.The third chapter, by setting an initial perturbation v(t, x) = u(t, x)- ?(x1) we simplify the equation. And we introduce a priori estimate. On this basis, we get the proof of the stability of the initial-boundary value problem and the algebraic convergence when the solution tends to stationary wave.The fourth chapter, we discuss the proof of time weighted energy estimates.The fifth chapter, based on time weighted energy estimates, we discuss the proof of space-time weighted energy estimates and the priori estimates.