ON A NON-CLASSICAL BOUNDARY VALUE PROBLEM FOR THE HEAT EQUATION.

In this paper, we are concerned in a non-classical boundary value problem for heat equation. More precisely, we study a linear heat equation without initial condition but with a homogeneous Dirichlet condition on the whole boundary and a nonhomogeneous Neumann condition on a part of the boundary. Under sufficient conditions on the data, we prove that the problem has a unique solution. The proof combines optimal control and controllability theories. [ABSTRACT FROM AUTHOR]