Analysis of degenerate Burgers' equations involving small perturbation and large wave amplitude

Abstract

We only focus on the shock waves to Burgers system by considering the porous medium diffusion and singularity in energy estimates. In this paper, the conditions (Figure presented.) and (Figure presented.) are considered. Moreover, we establish the existence of shock waves through the phase plane. The weighted function is employed to handle the singularity in the weighted energy estimates under small perturbations and arbitrary wave amplitudes. Finally, the weighted energy estimates are then used to prove the stability of shock waves.