A modified quasi-boundary value method for ill-posed problems

  • Denche M
  • Bessila K
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In this paper, we study a final value problem for first order abstract differential equation with positive self-adjoint unbounded operator coefficient. 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 and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates. © 2004 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Final value problem
  • Ill-posed problem
  • Quasi-boundary value problem
  • Quasireversibility methods

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  • M. Denche

  • K. Bessila

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