Assume we have the following system of balance laws: $$ U_t+\partial_x F(U,x)=S(U,x)+\partial_x(D(U,x)U_x). $$
Is there any method to analyse the stability of its solution (assume that the solution exists)? Here the dependence on $x$ is crucial, otherwise one at least could do the Fourier analysis after linearisation. It is really appreciated if one even can introduce a related paper.
Thanks!
