Mathematical Problems in Engineering 
Volume 7 (2001), Issue 2, Pages 129-145
doi:10.1155/S1024123X01001570

Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition

M. Denche and K. Bessila

 Departement de Mathematiques, Laboratoire: Equations Differentielles, Université Mentouri Constantine, Constantine 25000, Algeria
Received 3 October 2000

Abstract

In this paper we study the problem of control by the initial conditions of the heat equation with an integral boundary condition. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.