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

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  • M. Denche
  • K. Bessila

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.

Suggested Citation

  • M. Denche & K. Bessila, 2001. "Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition," Mathematical Problems in Engineering, Hindawi, vol. 7, pages 1-17, January.
    • Handle: RePEc:hin:jnlmpe:747249
    DOI: 10.1155/S1024123X01001570
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