(Cross-posted from Math.SE)

Suppose I have the Fokker-Planck PDE: $$ \frac{\partial}{\partial t}u(x,t)=-\frac{\partial}{\partial x}(\mu(x,t)u(x,t))+\frac{1}{2}\frac{\partial^2}{\partial x^2}(D(x,t)u(x,t)). $$ Denote the solution $u$ as $u^\mu$ to strength the fact that, in particular, it depends on $\mu$.

**Where can I find results that guarantee the continuity of the PDE solution with respect to the coefficients?**

That is, results guaranteeing that
$$
\mu_n(x,t)\to \mu(x,t) \implies u^{\mu_n}(x,t)\to u^{\mu}(x,t),
$$
under some conditions and appropriate definitions for the above convergences. The *simpler* the result, the *better*.