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

Volume 16, Number 2 (2014), 59 - 71

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

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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.