一类非散度型退化抛物方程源项反演问题
Inversion Problem of Source Term for a Class of Degenerate Parabolic Equations with Non-Divergent Form
摘要: 利用终端观测值，研究了非散度型退化抛物方程中重构源项的反问题。基于最优控制理论，将反问题转换为了最优控制问题。建立了控制泛函极小元的存在性和必要条件，并由必要条件得到了最优问题的局部唯一性和稳定性。
Abstract: Using terminal observations, the inverse problem of reconstructing source terms in non-divergent degenerate parabolic equations is studied. Based on optimal control theory, the inverse problem is transformed into an optimal control problem. The existence and necessary conditions of control functional are established. The local uniqueness and stability of the optimal problem are obtained from the necessary conditions.
文章引用：依力哈木江·依木马. 一类非散度型退化抛物方程源项反演问题[J]. 应用数学进展, 2022, 11(5): 3175-3184. https://doi.org/10.12677/AAM.2022.115336

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