Asymptotic Behaviors And Decay Rate Estimates Of Solutions For The Initial-Boundary Value Problems Of Scalar Viscous Conservation Laws

This thesis is concerned with the asymptotic behaviors and decay rate estimates of solutions for the initial-boundary value problems of scalar viscous conservation laws.For the initial-boundary value problems of scalar viscous conservation laws in one dimensional half-space with general boundary effect and small perturbation for the initial data, by using Lp-energy methods and L1-estimates, it is proved that the solution of the corresponding initial-boundary value problem converges time-asympotically to the linear superposition of the stationary wave and the rarefaction wave and an Lp-decay estimates is obtained under the condition that the flux function f is convex or non-convex.For the initial-boundary value problems of scalar viscous conservation laws in two dimensionals half-space with plane boundary effect and small perturbation for the initial data, by using L2-energy methods and L1-estimates, it is proved that the solution of the corresponding initial-boundary value problem converges time-asympotically to the planar rarefaction wave and an L2-decay estimates is obtained under the condition that the flux function f,g are sufficiently smooth and f is convex.