On a Non-classical Boundary Value Problem for the Heat Equation

Abstract

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.