A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination

Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form

“…In case = 1, the well posedness of IP1 was proved in [8]. Partial results were deduced earlier in [9].…”

Reconstruction of a Source Term in a Parabolic Integro-Differential Equation From Final Data

“…Recently some papers appeared that deal with the reconstruction of source terms or coefficients of these equations making use of final or integral overdetermination [5,12]. In particular, the authors' paper [5] extends former existence and uniqueness results of Isakov [3] to the integro-differential case. The existence of the solutions to the inverse problems to determine unknown source terms from final over-determination of the temperature requires sufficient regularity and a certain monotonicity of a time-component of this term.…”

“…In [5] we proved that in a particular case the solution of the inverse problem under consideration continuously depends on certain derivatives of the data.…”

“…We are going to estimate F . To this end, we make use of the following inequality that immediately follows from the estimate (19) in [5]:…”

Inverse Problems for a Generalized Subdiffusion Equation With Final Overdetermination

“…We prove the uniqueness of the solution to IP1 by applying a modified version of the positivity principle from [15]. That falls into category of maximum principle results [13,20,22]. Similar approaches to the inverse problems are well-known in the domain of parabolic equations [2,12].…”