metadata only access

https://hdl.handle.net/2115/91044

Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior

英語

short-time asymptotic behavior

2022-12-29

IOP Publishing

Inverse problems

39(2)

24003

As the most significant difference from parabolic equations, long-time or short-time behavior of solutions to time-fractional evolution equations is dominated by the fractional orders, whose unique determination has been frequently investigated in literature. Unlike all the existing results, in this article we prove the uniqueness of orders and parameters (up to a multiplier for the latter) only by principal terms of asymptotic expansions of solutions near t = 0 at a single spatial point. Moreover, we discover special conditions on unknown initial values or source terms for the coincidence of observation data. As a byproduct, we can even conclude the uniqueness for initial values or source terms by the same data. The proof relies on the asymptotic expansion after taking the Laplace transform and the completeness of generalized eigenfunctions.

学術雑誌論文

Accepted Manuscript

Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

0266-5611