Recovering initial population density of fractional pseudo-parabolic problem associated with a nonlinear reaction

In this paper, we consider an inverse problem related to the fractional pseudo-parabolic equation with a nonlinear source term. Our investigation reveals the ill-posedness of the problem according to Hadamard’s definition. We present two improved variations of the optimal filtering method introduced...

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Bibliographic Details
Published in:Journal of pseudo-differential operators and applications 2024-09, Vol.15 (3), Article 56
Main Authors: Minh, Triet Le, Quoc, Tu Tran, Hong, Phong Luu
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Analysis
Applications of Mathematics
Exact solutions
Functional Analysis
Inverse problems
Mathematics
Mathematics and Statistics
Operator Theory
Partial Differential Equations
Population density
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Summary:In this paper, we consider an inverse problem related to the fractional pseudo-parabolic equation with a nonlinear source term. Our investigation reveals the ill-posedness of the problem according to Hadamard’s definition. We present two improved variations of the optimal filtering method introduced by Seidman (SIAM J Numer Anal 33:162–170, 1996) to establish some optimal estimates under some an a priori assumptions on the regularity of the exact solution. Finally, the effectiveness of our algorithm is demonstrated through numerical examples.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-024-00632-z