摘要
This paper is concerned with the asymptotic behaviors of solutions of thegeneral initial-boundary value problem to scalar viscous conservation law uxx on R+ with the conditions u（0, t） = u-（t） u-（t ）,u（x,0） = u0（x） u+（x-）, where f"（u） > 0 for all u under consideration, u- < u+, and u--（t） u（R+）, Here the corresponding Riemann problem 0, u0（x） = u- when x <0 and u0（x）=u+ when x > 0 admits the rarefaction wave. Ourproblem is divided into five cases depending on the signs of the characteristic speeds of the boundary state u- at t= and the far field state u+ = u（+）. Both the globalexistence of the solution and the asymptotic stability are shown in all cases.
This paper is concerned with the asymptotic behaviors of solutions of thegeneral initial-boundary value problem to scalar viscous conservation law uxx on R+ with the conditions u(0, t) = u-(t) u-(t ),u(x,0) = u_0(x) u+(x-), where f'(u) > 0 for all u under consideration, u- < u+, and u--(t) u(R+), Here the corresponding Riemann problem 0, u0(x) = u- when x <0 and u0(x)=u+ when x > 0 admits the rarefaction wave. Ourproblem is divided into five cases depending on the signs of the characteristic speeds of the boundary state u- at t= and the far field state u+ = u(+). Both the globalexistence of the solution and the asymptotic stability are shown in all cases.
