Viscous Burgers equation (source code)

= 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>.