I should study some parabolic PDEs, but I'm not an expert, so I would like to ask your advice. First, could you give me some useful references concerning PARABOLIC PDES? I started reading DiBenedetto's book, but I didn't find what I needed.
My problem is to understand if a solution to the following does exist
$$\begin{cases} -u_t-\Delta u=f\qquad\text{for } (x,t)\in{\Omega}\times(0,T)\\ u(x,T)=0\qquad\text{for } x\in{\Omega}\\ \nabla u\cdot \nu=0\qquad\text{for } x\in\partial\Omega\times(0,T) \end{cases}$$
have you any idea? Which conditions the function $f$ has to satisfy?