Geodesic
Filter regularization for an inverse parabolic problem in several variables
Electronic journal of differential equations, Tome 2016 (2016)
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__a64,
     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},
     year = {2016},
     volume = {2016},
     zbl = {1336.65105},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a64/}
}
TY  - JOUR
AU  - Tuan,  Nguyen Huy
AU  - Kirane,  Mokhtar
AU  - Le,  Long Dinh
AU  - Van Nguyen,  Thinh
TI  - Filter regularization for an inverse parabolic problem in several variables
JO  - Electronic journal of differential equations
PY  - 2016
VL  - 2016
UR  - http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a64/
LA  - en
ID  - EJDE_2016__2016__a64
ER  - 
%0 Journal Article
%A Tuan,  Nguyen Huy
%A Kirane,  Mokhtar
%A Le,  Long Dinh
%A Van Nguyen,  Thinh
%T Filter regularization for an inverse parabolic problem in several variables
%J Electronic journal of differential equations
%D 2016
%V 2016
%U http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a64/
%G en
%F EJDE_2016__2016__a64
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__a64/