The Asymptotic Behaviors Of Solutions For The Relaxation Model With Boundary Effect

This thesis is concerned with the asymptotic behaviors of solutions for the relaxation model with boundary effect.Under the condition that the initial-boundary disturbance is large, using an L~2 -energy method and a technique of modifying boundary data proves that the solution of initial-boundary value problem to this semilinear relaxation model in one dimension with general boundary data effect converges time-asymptotically to a strong rarefaction wave.For the initial-boundary value problem to this semilinear relaxation model in two dimensions with constant boundary data effect, it is proved that the solution of this problem converges time-asymptotically to a strong planar rarefaction wave for small initial disturbance by an L~2 -energy method.