Convergence to traveling waves with decay rates for solutions of the initial boundary problem to a relaxation model

tn this paper we consider a 2 x 2 relaxation hyperbolic system of conservation laws with a boundary effect. and we show that the solutions of this initial boundary problem tend to the traveling wave solutions of the corresponding Cauchy problem time-asymptotically, In particular, we give the algebraic and exponential decay rates by using the weighted energy method. The location of a shift. for the traveling wave. to overcome the difficulty in the boundary, plays a key role in this paper. (C) 1999 Academic Press.