Convergence to shock profiles for Burgers equation with singular fast-diffusion and boundary effect

Xiaowen Li, Ming Mei

In this paper, we study the asymptotic stability of viscous shock profile for the Burgers equation $u_t+f(u{)}_x=(\frac{u_x}{u^{1-m}}{)}_x$ on the half-space $(0,+\infty )$, subjec…