Simultaneous identification of the initial data in a degenerate and singular hyperbolic wave equation

被引：0

作者：

Zafrar, Abderrahim ^{[1
]}

Boutaayamou, Idriss ^{[2
]}

Ouakrim, Youssef ^{[3
]}

Salhi, Jawad ^{[4
]}

机构：

[1] Univ Sidi Mohamed Ben Abdellah, Fac Sci Dhar El Mahraz, Dept Math, Atlas Fez 30003, Morocco

[2] Ibnou Zohr Univ, Fac Ouarzazate, Lab SIV Polydisciplinary, Ouarzazate 45000, Morocco

[3] Univ Sidi Mohamed Ben Abdellah, Ecole Normale Super, Lab Math Modelisat & Phys Appl, Fes, Morocco

[4] Moulay Ismail Univ Meknes, MAIS Lab, MAMCS Grp, FST Errachidia, POB 509, Errachidia 52000, Morocco

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2025年 / 44卷 / 01期

关键词：

Inverse problem; Degenerate hyperbolic equations; Singular hyperbolic equations; Tikhonov regularization; Nonlinear optimization; AUGMENTED LAGRANGIAN METHOD; COEFFICIENT IDENTIFICATION; BOUNDARY CONTROLLABILITY; PARAMETER-IDENTIFICATION; DISCONTINUOUS PARAMETERS; PARABOLIC EQUATIONS; ELLIPTIC-EQUATIONS; RECONSTRUCTION; STABILIZATION; INEQUALITIES;

D O I：

10.1007/s40314-024-02975-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the determination of the initial data in a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. In particular, we address the question of well posedness of the problem. Then, the identification of the initial data is formulated as a minimization problem combining the output least squares method and the Tikhonov regularization. Finally, numerical results are provided to show the performance of the proposed approach.

引用

页数：24

共 50 条

[31] Degenerate wave equation with localized initial data: Asymptotic solutions corresponding to various self-adjoint extensions
V. E. Nazaikinskii
Mathematical Notes, 2011, 89 : 749 - 753
[32] Degenerate wave equation with localized initial data: Asymptotic solutions corresponding to various self-adjoint extensions
Nazaikinskii, V. E.
MATHEMATICAL NOTES, 2011, 89 (5-6) : 749 - 753
[33] SINGULAR PERTURBATIONS FOR A SEMILINEAR HYPERBOLIC EQUATION
HSIAO, GC
WEINACHT, RJ
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1983, 14 (06) : 1168 - 1179
[34] Optimal decay-error estimates for the hyperbolic-parabolic singular perturbation of a degenerate nonlinear equation
Ghisi, Marina
Gobbino, Massimo
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (02) : 911 - 932
[35] AN ASYMPTOTIC METHOD FOR A SINGULAR HYPERBOLIC EQUATION
MEYER, RE
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1966, 22 (03) : 185 - &
[36] On singular perturbation of a semilinear hyperbolic equation
Koiso, N
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1996, 4 (01) : 89 - 101
[37] Generalized solution of Schrodinger equation with singular potential and initial data
Benmerrous, Abdelmjid
Chadli, Lalla Saadia
Moujahid, Abdelaziz
Elomari, M'hamed
Melliani, Said
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (01): : 3093 - 3101
[38] The Cauchy problem for a semilinear heat equation with singular initial data
Ruf, B
Terraneo, E
EVOLUTION EQUATIONS, SEMIGROUPS AND FUNCTIONAL ANALYSIS: IN MEMORY OF BRUNELLO TERRENI, 2002, 50 : 295 - 309
[39] A singular solution with smooth initial data for a semilinear parabolic equation
Sato, Shota
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (04) : 1383 - 1392
[40] Identification for degenerate problems of hyperbolic type
Favini, Angelo
Marinoschi, Gabriela
APPLICABLE ANALYSIS, 2012, 91 (08) : 1511 - 1527

← 1 2 3 4 5 →