Stability and numerical analysis of backward problem for subdiffusion with time-dependent coefficients

نویسندگان

چکیده

Abstract Our aim is to study the backward problem, i.e. recover initial data from terminal observation, of subdiffusion with time dependent coefficients. First all, by using smoothing property solution operators and a perturbation argument freezing diffusion coefficients, we show stability estimate in Sobolev spaces, under some smallness/largeness condition on time. Moreover, case noisy data, apply quasi-boundary value method regularize problem then convergence regularization scheme. Finally, propose completely discrete scheme applying finite element space Euler convolution quadrature An priori error established. The proof heavily built dealing coefficients nonstandard estimates for direct problem. gives an useful guide balancing discretization parameters, parameter noise level. Some numerical experiments are presented illustrate our theoretical results.

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ژورنال

عنوان ژورنال: Inverse Problems

سال: 2023

ISSN: ['0266-5611', '1361-6420']

DOI: https://doi.org/10.1088/1361-6420/acb007