{"id":5466,"date":"2023-06-07T09:21:05","date_gmt":"2023-06-07T09:21:05","guid":{"rendered":"https:\/\/iamm.in.ua\/?p=5466"},"modified":"2023-10-11T12:11:07","modified_gmt":"2023-10-11T09:11:07","slug":"seminar-contemporary-analysis-and-partial-differential-equations-20-06-2023","status":"publish","type":"post","link":"https:\/\/iamm.in.ua\/?p=5466&lang=en","title":{"rendered":"SEMINAR \u201cContemporary Analysis and Partial Differential Equations\u201d (20.06.2023)"},"content":{"rendered":"

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Jaan Janno<\/strong><\/span><\/p>\n

Tallinn University of Technology, Estonia<\/span><\/p>\n

jaan.janno@taltech.ee<\/span><\/p>\n

On some inverse problems that use nonlocality of fractional derivatives<\/em><\/strong><\/span><\/p>\n

Tuesday, 20 June 2023 at 13:00<\/span><\/p>\n

On line: https:\/\/meet.google.com\/nif-zfwd-mrg<\/a><\/span><\/p>\n

Abstract<\/strong><\/span><\/p>\n

We consider some inverse problems for time-fractional diffusion equation of the order between 0<\/span> and 1<\/span>. In the first class of problems, time-dependent source factors are reconstructed from final data. The proof of uniqueness uses power-type asymptotics of Mittag-Leffler functions involved in solution formulas of corresponding direct problems. This is related to the nonlocality of the fractional derivative included in the diffusion equation. In the second class of problems, the data are given in an arbitrarily small time neighborhood of the final value. Then, due to the nonlocality of a fractional derivative, a function given in a such neighborhood can be extended backward in time to the initial time value provided the fractional derivative of this function is also given in the mentioned neighborhood. This basic result is applied to some inverse problems of reconstruction of time- and space-dependent sources.<\/span><\/p>\n

Seminar video report<\/span><\/p>\n