Geodesic
Null controllability of degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain
Eurasian journal of mathematical and computer applications, Tome 8 (2020) no. 1, pp. 4-29

Voir la notice de l'article provenant de la source Math-Net.Ru

The main purpose of this work is to study numerically a null controllability for a class of one-dimensional degenerate/singular parabolic equations, in divergence and nondivergence form. For this, we resolve an inverse source problem reformulated in a least-squares framework, which leads to a non-convex minimization problem of a cost function $J$, that is solved using a Tikhonov regularization. Firstly, we prove the well-posedness of the minimization problem and the direct problem. Secondly we prove the differentiability of the functional $J$, which gives the existence of the gradient of $J$, that is computed using the adjoint state method. Finally, to show the convergence of the descent method, we prove the Lipschitz continuity of the gradient of $J$. Also we present some numerical experiments.
Keywords: Null controllability, singular equations, inverse source problem, adjoint-state method. 
@article{EJMCA_2020_8_1_a0,
     author = {Kh. Atifi and E.-H. Essoufi and B. Khouiti},
     title = {Null controllability of degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {4--29},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2020_8_1_a0/}
}
TY  - JOUR
AU  - Kh. Atifi
AU  - E.-H. Essoufi
AU  - B. Khouiti
TI  - Null controllability of degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain
JO  - Eurasian journal of mathematical and computer applications
PY  - 2020
SP  - 4
EP  - 29
VL  - 8
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJMCA_2020_8_1_a0/
LA  - en
ID  - EJMCA_2020_8_1_a0
ER  - 
%0 Journal Article
%A Kh. Atifi
%A E.-H. Essoufi
%A B. Khouiti
%T Null controllability of degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain
%J Eurasian journal of mathematical and computer applications
%D 2020
%P 4-29
%V 8
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJMCA_2020_8_1_a0/
%G en
%F EJMCA_2020_8_1_a0
Kh. Atifi; E.-H. Essoufi; B. Khouiti. Null controllability of degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Eurasian journal of mathematical and computer applications, Tome 8 (2020) no. 1, pp. 4-29. http://geodesic.mathdoc.fr/item/EJMCA_2020_8_1_a0/