The delta-shock wave for the two variables of a class of Temple system

We investigate the Riemann problem for one-dimensional Temple class, obtain the Riemann solutions containing delta-shock wave, and discover that each variable of this system contains the Dirac delta function in different region. By the interaction of the delta-shock wave with the elementary waves we present the generalized Riemann problem for this system and construct the global solutions. By studying the limits of the solutions as perturbed parameter e approaches zero we observe that the Riemann solutions are stable for such perturbations of the initial data.