Improved Regularization Method for Backward Cauchy Problems Associated with Continuous Spectrum Operator
Joint Authors
Source
International Journal of Differential Equations
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-11-22
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We consider in this paper an abstract parabolic backward Cauchy problem associated with an unbounded linear operator in a Hilbert space H, where the coefficient operator in the equation is an unbounded self-adjoint positive operator which has a continuous spectrum and the data is given at the final time t=T and a solution for 0≤t It is well known that this problem is illposed in the sense that the solution (if it exists) does not depend continuously on the given data. The method of regularization used here consists of perturbing both the equation and the final condition to obtain an approximate nonlocal problem depending on two small parameters. We give some estimates for the solution of the regularized problem, and we also show that the modified problem is stable and its solution is an approximation of the exact solution of the original problem. Finally, some other convergence results including some explicit convergence rates are also provided.
American Psychological Association (APA)
Djezzar, Salah& Teniou, Nihed. 2011. Improved Regularization Method for Backward Cauchy Problems Associated with Continuous Spectrum Operator. International Journal of Differential Equations،Vol. 2011, no. 2011, pp.1-11.
https://search.emarefa.net/detail/BIM-507565
Modern Language Association (MLA)
Djezzar, Salah& Teniou, Nihed. Improved Regularization Method for Backward Cauchy Problems Associated with Continuous Spectrum Operator. International Journal of Differential Equations No. 2011 (2011), pp.1-11.
https://search.emarefa.net/detail/BIM-507565
American Medical Association (AMA)
Djezzar, Salah& Teniou, Nihed. Improved Regularization Method for Backward Cauchy Problems Associated with Continuous Spectrum Operator. International Journal of Differential Equations. 2011. Vol. 2011, no. 2011, pp.1-11.
https://search.emarefa.net/detail/BIM-507565
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-507565