2
votes
1answer
100 views

Heat transfer: boundary conditions with fluid velocity

The following equation is considered: $$ \frac{\partial u}{\partial t} - a\Delta u + \mathbf v \cdot \nabla u = f. $$ I have difficulties in formulating boundary conditions for this equation. If ...
5
votes
1answer
868 views

Short time existence on nonlinear parabolic PDE

I saw several papers that without proof accept the fact "Short time existence on nonlinear parabolic PDE" is there any affirmative proof of this fact? in which book we have this fact, the number of ...