Regularization methods for identifying the initial value of time fractional pseudo-parabolic equation

Yang, Fan; Xu, Jian-Ming; Li, Xiaoxiao

doi:10.1007/s10092-022-00492-3

Cited by 4 publications

(1 citation statement)

References 29 publications

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“…Later, in [18], Boussetila and Rebbani gave the modified quasi-inverse regularization method to solve the ill-posed problem of unbounded linear operators in Hilbert Spaces. In [19], a regularization method combining the improved quasi-inverse and the improved quasi-boundary is used to identify both the source term and the initial value of space-time fractional diffusion equation. In order to solve the ill-posed problem more easily, a new regularization method, modified quasi-initial regularization method, is proposed in this paper.…”

Section: Introductionmentioning

confidence: 99%

A hybrid regularization method for identifying the source term and the initial value simultaneously for fractional pseudo-parabolic equations with involution *

Liang,

Yang,

2024

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In this paper, we study the problem of identifying source term and initial value simultaneously for fractional pseudo-parabolic equations with involution. This is an ill-posed problem and the conditional stability is given. A hybrid regularization method, which combines the modified quasi-inverse and the modified quasi-initial value, is used to deal with the inverse problem. The error estimates of the exact solution and the regularization solution are given respectively under the priori and the posteriori regularization parameter choice rules. Several numerical examples are presented to certify the hybrid regularization method is effective.

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Section: Introductionmentioning

confidence: 99%