Filter Regularization Method for Inverse Source Problem of the Rayleigh–Stokes Equation

Liu, Songshu

doi:10.11650/tjm/230302

Cited by 2 publications

(1 citation statement)

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“…In [21], the authors provide the existence and regularity of the inverse problem for the nonlinear fractional Rayleigh-Stokes equations. In [22,23], the authors give a Tikhonov regularization method and filter regularization method to identify the source term for the Rayleigh-Stokes problem. In [24], the authors use the trigonometric method in nonparametric regression associated to regularize the instable solution of the initial inverse problem for the nonlinear fractional Rayleigh-Stokes equation with random discrete data.…”

Section: Introductionmentioning

confidence: 99%

On a Backward Problem for the Rayleigh–Stokes Equation with a Fractional Derivative

Liu,

2023

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The Rayleigh–Stokes equation with a fractional derivative is widely used in many fields. In this paper, we consider the inverse initial value problem of the Rayleigh–Stokes equation. Since the problem is ill-posed, we adopt the Tikhonov regularization method to solve this problem. In addition, this paper not only analyzes the ill-posedness of the problem but also gives the conditional stability estimate. Finally, the convergence estimates are proved under two regularization parameter selection rules.

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Section: Introductionmentioning

confidence: 99%

On a Backward Problem for the Rayleigh–Stokes Equation with a Fractional Derivative

Liu,

2023

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A Fractional Tikhonov Regularization Method for Identifying a Time-Independent Source in the Fractional Rayleigh–Stokes Equation

Liu,

Feng,

Liu

2024

Fractal Fract

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The aim of this paper is to identify a time-independent source term in the Rayleigh–Stokes equation with a fractional derivative where additional data are considered at a fixed time point. This inverse problem is proved to be ill-posed in the sense of Hadamard. By using a fractional Tikhonov regularization method, we construct a regularized solution. Then, according to a priori and a posteriori regularization parameter selection rules, we prove the convergence estimates of the regularization method. Finally, we provide some numerical examples to prove the effectiveness of the proposed method.

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Filter Regularization Method for Inverse Source Problem of the Rayleigh–Stokes Equation

Cited by 2 publications

References 12 publications

On a Backward Problem for the Rayleigh–Stokes Equation with a Fractional Derivative

On a Backward Problem for the Rayleigh–Stokes Equation with a Fractional Derivative

A Fractional Tikhonov Regularization Method for Identifying a Time-Independent Source in the Fractional Rayleigh–Stokes Equation

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