Inverse problem for a degenerate/singular parabolic system with Neumann boundary conditions-Reference-Cited by-同舟云学术

Inverse problem for a degenerate/singular parabolic system with Neumann boundary conditions

Published:2020-11-18 Issue:6 Volume:29 Page:791-821
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Alaoui Mohammed¹,Hajjaj Abdelkarim¹,Maniar Lahcen²,Salhi Jawad¹

Affiliation:

1. Laboratoire MISI , Faculté des Sciences et Techniques , Hassan First University of Settat , BP 577 , Settat , Morocco

2. LMDP, UMMISCO (IRD-UPMC), Faculté des Sciences Semlalia , Cadi Ayyad University , Marrakech 40000, B.P. 2390 , Morocco

Abstract

Abstract In this paper, we study an inverse source problem for a degenerate and singular parabolic system where the boundary conditions are of Neumann type. We consider a problem with degenerate diffusion coefficients and singular lower-order terms, both vanishing at an interior point of the space domain. In particular, we address the question of well-posedness of the problem, and then we prove a stability estimate of Lipschitz type in determining the source term by data of only one component. Our method is based on Carleman estimates, cut-off procedures and a reflection technique.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2018-0034/pdf

Reference38 articles.

1. E. M. Ait Ben Hassi, F. Ammar Khodja, A. Hajjaj and L. Maniar, Null controllability of degenerate parabolic cascade systems, Port. Math. 68 (2011), no. 3, 345–367.

2. E. M. Ait Ben Hassi, F. Ammar Khodja, A. Hajjaj and L. Maniar, Carleman estimates and null controllability of coupled degenerate systems, Evol. Equ. Control Theory 2 (2013), no. 3, 441–459.

3. F. Alabau-Boussouira, P. Cannarsa and G. Fragnelli, Carleman estimates for degenerate parabolic operators with applications to null controllability, J. Evol. Equ. 6 (2006), no. 2, 161–204.

4. W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems, Monogr. Math. 96, Birkhäuser, Basel, 2001.

5. P. Baras and J. A. Goldstein, Remarks on the inverse square potential in quantum mechanics, Differential Equations (Birmingham 1983), North-Holland Math. Stud. 92, North-Holland, Amsterdam (1984), 31–35.