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Harrach, Bastian (ed.); Kaltenbacher, Barbara (ed.); Rundell, William (ed.)

Special issue on inverse problems for fractional operators. (English) Zbl 1543.00011

Inverse Probl. 40, No. 9, Article ID 090201, 4 p. (2024).
From the text: A series of papers in this special issue studies inverse problems for time fractional differential equations: Reconstruction of the fractional order is a practically important modeling task and can mathematically be very well based on short and long time asymptotics of solutions to time fractional equations. Further practically highly relevant questions that have recently found much attention are (a) How much information on the model (e.g. initial data) can be omitted? (b) Which parts of the model can be determined in addition to the fractional order?

MSC:

00B15 Collections of articles of miscellaneous specific interest
35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
65-06 Proceedings, conferences, collections, etc. pertaining to numerical analysis
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References:

[1] Antil, H.; Wachsmuth, D., Sparse optimization problems in fractional order Sobolev spaces, Inverse Problems, 39, 2023 · Zbl 1510.35352 · doi:10.1088/1361-6420/acbe5e
[2] Cen, S.; Jin, B.; Liu, Y.; Zhou, Z., Recovery of multiple parameters in subdiffusion from one lateral boundary measurement, Inverse Problems, 39, 2023 · Zbl 1540.35464 · doi:10.1088/1361-6420/acef50
[3] Jin, B.; Shin, K.; Zhou, Z., Numerical recovery of a time-dependent potential in subdiffusion*, Inverse Problems, 40, 2023 · Zbl 1531.35394 · doi:10.1088/1361-6420/ad14a0
[4] Kian, Y.; Soccorsi, E., Solving time-fractional diffusion equations with a singular source term, Inverse Problems, 39, 2023 · Zbl 1526.35290 · doi:10.1088/1361-6420/ad0176
[5] Lassas, M.; Li, Z.; Zhang, Z., Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems, Inverse Problems, 39, 2023 · Zbl 1518.35678 · doi:10.1088/1361-6420/acdab9
[6] Liu, Y.; Yamamoto, M., Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior, Inverse Problems, 39, 2022 · Zbl 1505.35370 · doi:10.1088/1361-6420/acab7a
[7] Slodička, M., Some direct and inverse source problems in nonlinear evolutionary PDEs with Volterra operators, Inverse Problems, 38, 2022 · Zbl 1501.35428 · doi:10.1088/1361-6420/ac95bb
[8] Yamamoto, M., Uniqueness for inverse source problems for fractional diffusion-wave equations by data during not acting time, Inverse Problems, 39, 2023 · Zbl 1505.35372 · doi:10.1088/1361-6420/aca55c
[9] Zhang, Z.; Zhou, Z., Stability and numerical analysis of backward problem for subdiffusion with time-dependent coefficients, Inverse Problems, 39, 2023 · Zbl 1507.35346 · doi:10.1088/1361-6420/acb007
[10] Zimmermann, P., Inverse problem for a nonlocal diffuse optical tomography equation, Inverse Problems, 39, 2023 · Zbl 1537.35423 · doi:10.1088/1361-6420/ace4ed
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