Inverse Problem of Determining the Absorption Coefficient in a Degenerate Parabolic Equation in the Class L ∞

2021 ◽  
Vol 61 (3) ◽  
pp. 388-402
Author(s):  
V. L. Kamynin
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Absorption Coefficient ◽  
Degenerate Parabolic Equation ◽  
Degenerate Parabolic

Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation

2020 ◽  
Vol 18 (01) ◽  
pp. 2050032
Author(s):  
M. Alahyane ◽  
I. Boutaayamou ◽  
A. Chrifi ◽  
Y. Echarroudi ◽  
Y. Ouakrim
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
Augmented Lagrangian ◽  
Numerical Study ◽  
Augmented Lagrangian Method ◽  
Inverse Source Problem ◽  
Discrete Solution ◽  
Degenerate Parabolic

This paper is devoted to numerical analysis of an inverse source problem in a degenerate parabolic equation. The aims of this work are to show the well-posedness of the discrete inverse problem and its convergence to the continuous one. For this, we reformulate first the encountered inverse problem to a regularized optimal control one. Then, we approximate our optimal control problem by finite element method and we show the existence of the discrete solution and its convergence to the continuous one. Finally, in order to confirm the efficiency of the proposed scheme, some numerical results are obtained using the augmented Lagrangian method.

Sign in / Sign up

Export Citation Format

Share Document