Identification of source terms in wave equation with dynamic boundary conditions

Chorfi, Salah-Eddine; Guermai, G. El; Maniar, Lahcen; Walid, Zouhair,

doi:10.1002/mma.8556

Cited by 6 publications

(2 citation statements)

References 53 publications

(84 reference statements)

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“…The existence and necessary conditions for the minimization of the objective function were obtained, and numerical results were obtained by applying the projected gradient method and the two-parameter model function method to the minimization problem. Chorfi-El Guermai-Maniar-Zouhair [10] investigated a class of inverse hyperbolic problems for the wave equation with dynamic boundary conditions. The main objective was to determine some forcing terms from the final overdetermination of the displacement.…”

Section: Introductionmentioning

confidence: 99%

Source Inversion Based on Distributed Acoustic Sensing-Type Data

Shen,

Wang,

Zhang

2024

Mathematics

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In this study, we investigate the inverse problem of the two-dimensional wave equation source term, which arises from the Distributed Acoustic Sensing (DAS) data on the boundary. We construct a new integral operator that maps the interior sources to the DAS-type data at the boundary. Due to the noninjectivity and instability of the integral operator, which violates the well posedness of the inverse problem, a minimization problem on a compact convex subset is formulated, and the existence and uniqueness of the minimizer are obtained. Numerical examples for different cases are illustrated.

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Section: Introductionmentioning

confidence: 99%

Source Inversion Based on Distributed Acoustic Sensing-Type Data

Shen,

Wang,

Zhang

2024

Mathematics

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“…This is exactly where the inverse problems theory comes in. More precisely, inverse problems theory consists of identifying some input parameters in a given system from a partial measurement on the solution, e.g., forcing terms [13,14,17], thermal conductivity and radiative coefficient [15], potential, damping coefficient and source terms [5,6,8], or initial temperature [21]. Up to our knowledge, the most practical and realistic measurements considered in literature use the state at a fixed final time.…”

Section: Introductionmentioning

confidence: 99%

Numerical identification of initial temperatures in heat equation with dynamic boundary conditions

Chorfi¹,

Guermai²,

Maniar³

et al. 2022

Preprint

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We investigate the inverse problem of numerically identifying unknown initial temperatures in a heat equation with dynamic boundary conditions whenever some overdetermination data is provided after a final time. This is a backward parabolic problem which is severely ill-posed. As a first step, the problem is reformulated as an optimization problem with an associated cost functional. Using the weak solution approach, an explicit formula for the Fréchet gradient of the cost functional is derived from the corresponding sensitivity and adjoint problems. Then the Lipschitz continuity of the gradient is proved. Next, further spectral properties of the input-output operator are established. Finally, the numerical results for noisy measured data are performed using the regularization framework and the conjugate gradient method. We consider both one-and two-dimensional numerical experiments using finite difference discretization to illustrate the efficiency of the designed algorithm. Aside from dealing with a time derivative on the boundary, the presence of a boundary diffusion makes the analysis more complicated. This issue is handled in the 2-D case by considering the polar coordinate system. The presented method implies fast numerical results.

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