Action functional and quasi-potential for the Burgers equation in a bounded interval

Lorenzo Bertini, Alberto De Sole, Davide Gabrielli +2

Consider the viscous Burgers equation $u_t+f(u{)}_x=\epsilon u_{xx}$ on the interval $[0,1]$ with the inhomogeneous Dirichlet boundary conditions $u(t,0)={\rho }_0$, $u(t,1)={\rho }_1$. The f…