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In this talk, two inverse source problems for a one-dimensional, and for a multidimensional linear parabolic equations backward in time will be considered. In each of these problems, we recover a space-wise dependent source term from an overdetermination. Note that if the conditions with respect to time are given at $t \neq 0$, then the problems become some inverse problems of simultaneous recovery of the source and the initial condition. For the analysis of these problems, some stability estimates for their solutions will be presented in some Banach spaces. Furthermore, for the numerical solution of the problems some explicit finite difference schemes will be presented along with some stability estimates for their solutions. Finally, the proposed numerical methods will be performed on some test problems to acquire their initial conditions, sources, and solutions, simultaneously. Moreover, for showing the efficiency of the proposed methods a numerical analysis is given.

*The meeting id and the passcode will be emailed to the seminar mailing list.

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