Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation

Alahyane, Mohamed; Boutaayamou, Idriss; Chrifi, Abderrazak; Echarroudi, Younes; Ouakrim, Youssef

doi:10.1142/s0219876220500322

Cited by 3 publications

(2 citation statements)

References 45 publications

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“…The source function for a seawater intrusion problem in an unconfined aquifer has been studied by Slimani [8]. The inverse source problems were examined by Alahyane et al [9] using the regularized optimal control method. Some new regularization methods were proposed for inverse source problems governed by fractional PDEs [10,11].…”

Section: Introductionmentioning

confidence: 99%

Solving Inverse Conductivity Problems in Doubly Connected Domains by the Homogenization Functions of Two Parameters

et al. 2022

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In the paper, we make the first attempt to derive a family of two-parameter homogenization functions in the doubly connected domain, which is then applied as the bases of trial solutions for the inverse conductivity problems. The expansion coefficients are obtained by imposing an extra boundary condition on the inner boundary, which results in a linear system for the interpolation of the solution in a weighted Sobolev space. Then, we retrieve the spatial- or temperature-dependent conductivity function by solving a linear system, which is obtained from the collocation method applied to the nonlinear elliptic equation after inserting the solution. Although the required data are quite economical, very accurate solutions of the space-dependent and temperature-dependent conductivity functions, the Robin coefficient function and also the source function are available. It is significant that the nonlinear inverse problems can be solved directly without iterations and solving nonlinear equations. The proposed method can achieve accurate results with high efficiency even for large noise being imposed on the input data.

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Section: Introductionmentioning

confidence: 99%

Solving Inverse Conductivity Problems in Doubly Connected Domains by the Homogenization Functions of Two Parameters

et al. 2022

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“…The paper [24] has considered a similar problem with a regularizing parameter that approximates and regularizes the heat conduction model. More recently, the authors of [4] have analyzed numerically an inverse source problem in a degenerate parabolic equation. They have adapted an optimal control approach using finite element discretization and the augmented Lagrangian method.…”

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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Numerical Identification of Initial Temperatures in Heat Equation with Dynamic Boundary Conditions

et al. 2023

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Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation

Cited by 3 publications

References 45 publications

Solving Inverse Conductivity Problems in Doubly Connected Domains by the Homogenization Functions of Two Parameters

Solving Inverse Conductivity Problems in Doubly Connected Domains by the Homogenization Functions of Two Parameters

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

Numerical Identification of Initial Temperatures in Heat Equation with Dynamic Boundary Conditions

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