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On recovering space-dependent source term in a degenerate nonlocal parabolic equation | ||
| Journal of Mathematical Modeling | ||
| مقاله 10، دوره 13، شماره 3، مهر 2025، صفحه 645-662 اصل مقاله (356.13 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.29151.2596 | ||
| نویسندگان | ||
| Maroua Nouar؛ Abdeldjalil Chattouh* | ||
| ICOSI laboratory, Department of Mathematics, Khenchela University, Khenchela, Algeria | ||
| چکیده | ||
| Identifying the unknown source terms in diffusion models, including nonlocal ones, is an active research area with significant applications in engineering and scientific fields such as population dynamics, biology, and physics. This study examines an inverse problem focused on recovering a space-dependent source term in a degenerate diffusion model that includes a nonlocal space term, using final-time measured data. As a first step, the inverse problem is reformulated as an optimization one by considering its solution as the minimizer of a well-defined objective function. The existence of a unique solution to the associated direct problem is discussed in a functional framework based on suitable weighted Sobolev spaces. After that, we prove the existence of a minimizer by means of standard arguments, and establish a first-order necessary optimality condition. Using this last one, we obtain some results concerning the stability and local uniqueness property. For the numerical reconstruction of the missing source term, we designed an algorithm based on the Landweber iterative method and showed its effectiveness by providing several numerical tests. | ||
| کلیدواژهها | ||
| Inverse problem؛ identification problem؛ degenerate parabolic equation؛ optimal control؛ stability | ||
| مراجع | ||
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