Mathematical Problems in Engineering
Volume 7 (2001), Issue 2, Pages 129-145

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

Copyright © 2001 M. Denche and K. Bessila. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.