Academic Journal
The Carleman Contraction Mapping Method for a Coefficient Inverse Problem of the Epidemiology: The Carleman contraction mapping method for a coefficient inverse problem of the epidemiology
| Τίτλος: | The Carleman Contraction Mapping Method for a Coefficient Inverse Problem of the Epidemiology: The Carleman contraction mapping method for a coefficient inverse problem of the epidemiology |
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| Συγγραφείς: | Michael V. Klibanov, Trung Truong |
| Πηγή: | SIAM Journal on Applied Mathematics. 85:848-874 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Society for Industrial & Applied Mathematics (SIAM), 2025. |
| Έτος έκδοσης: | 2025 |
| Θεματικοί όροι: | monitoring epidemics, Inverse problems for PDEs, convexification, 35R30, Reaction-diffusion equations, Epidemiology, numerical studies, FOS: Mathematics, Initial-boundary value problems for second-order parabolic systems, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), coefficient inverse problem, Carleman estimate |
| Περιγραφή: | It is proposed to monitor spatial and temporal spreads of epidemics via solution of a Coefficient Inverse Problem for a system of three coupled nonlinear parabolic equations. To solve this problem numerically, a version of the so-called Carleman contraction mapping method is developed for this problem. On each iteration, a linear problem with the incomplete lateral Cauchy data is solved by the weighted Quasi-Reversibility Method, where the weight is the Carleman Weight Function. This is the function, which is involved as the weight in the Carleman estimate for the corresponding parabolic operator. Convergence analysis ensures the global convergence of this procedure. Numerical results demonstrate an accurate performance of this technique for noisy data. 26 pages |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1095-712X 0036-1399 |
| DOI: | 10.1137/24m1714356 |
| DOI: | 10.48550/arxiv.2412.00297 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2412.00297 |
| Rights: | arXiv Non-Exclusive Distribution |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....e205ad6d2a0740c943d0da04a0bb0ee7 |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 1095712X 00361399 |
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| DOI: | 10.1137/24m1714356 |