Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation

被引：3

作者：

Alahyane, M. ^{[1
]}

Boutaayamou, I ^{[2
]}

Chrifi, A. ^{[3
]}

Echarroudi, Y. ^{[4
]}

Ouakrim, Y. ^{[5
]}

机构：

[1] Univ Sharjah, Res Inst Sci & Engn, Sharjah, U Arab Emirates

[2] Ibn Zohr Univ, Polydisciplinary Fac Ouarzazate, Ouarzazate 45000, Morocco

[3] Cadi Ayyad Univ, Fac Sci & Tech, Marrakech 40000, Morocco

[4] Cadi Ayyad Univ, Fac Sci Semlalia, Lab Math & Populat Dynam, Marrakech 40000, Morocco

[5] Univ Sidi Mohammed Ben Abdellah, Ecole Normale Super Math Modelisat & Phys Appl, Fes 30000, Morocco

来源：

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS | 2021年 / 18卷 / 01期

关键词：

Inverse source problem; identification; degenerate parabolic equations; augmented Lagrangian method; optimal control; regularization; finite element method; AUGMENTED LAGRANGIAN METHOD; DIFFUSION-COEFFICIENT; CONVERGENCE-RATES; DISCONTINUOUS PARAMETERS; ELLIPTIC-EQUATIONS; IDENTIFICATION; RECONSTRUCTION; REGULARIZATION; OPTIMIZATION; TEMPERATURE;

D O I：

10.1142/S0219876220500322

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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.

引用

页数：22

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