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

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...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 301; no. 2; pp. 419 - 426
Main Authors: Denche, M., Bessila, K.
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 15.01.2005
Elsevier
Subjects:
Exact sciences and technology
Final value problem
Ill-posed problem
Mathematical analysis
Mathematics
Ordinary differential equations
Quasi-boundary value problem
Quasireversibility methods
Sciences and techniques of general use
Ill-posed problem
Quasireversibility methods
Quasi-boundary value problem
Final value problem
First order equation
Boundary value problem
Quasireversibility method
Mathematical analysis
Differential equation
Convergence rate
Well posed problem
Ill posed problem
Approximate solution
Self adjoint operator
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.08.001