Geodesic
Filter regularization for an inverse parabolic problem in several variables
Electronic Journal of Differential Equations, Tome 2016 (2016).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The backward heat problem is known to be ill possed, which has lead to the design of several regularization methods. In this article we apply the method of filtering out the high frequencies from the data for a parabolic equation. First we identify two properties that if satisfied they imply the convergence of the approximate solution to the exact solution. Then we provide examples of filters that satisfy the two properties, and error estimates for their approximate solutions. We also provide numerical experiments to illustrate our results.
Classification : 35K05, 35K99, 47J06, 47H10
Keywords: ill-posed problem, truncation method, heat equation, regularization 
@article{EJDE_2016__2016__a31,
     author = {Tuan, Nguyen Huy and Kirane, Mokhtar and Le, Long Dinh and Van Nguyen, Thinh},
     title = {Filter regularization for an inverse parabolic problem in several variables},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a31/}
}
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%A Van Nguyen, Thinh
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%J Electronic Journal of Differential Equations
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Tuan, Nguyen Huy; Kirane, Mokhtar; Le, Long Dinh; Van Nguyen, Thinh. Filter regularization for an inverse parabolic problem in several variables. Electronic Journal of Differential Equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a31/