Viscous Burgers equation
= Viscous Burgers equation
{title2=$u_t+uu_x=\nu u_{xx}$}
{wiki=Burgers'_equation}
The viscous Burgers equation adds diffusion with viscosity $\nu>0$ to nonlinear transport. Smooth initial data remain smooth, and the diffusion regularizes the shocks of the <Inviscid Burgers equation>.