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Recovering the source term for parabolic equation with nonlocal integral condition

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The main purpose of this article is to present a Tikhonov method to construct the source function f(x) of the parabolic diffusion equation. This problem is well known to be… Click to show full abstract

The main purpose of this article is to present a Tikhonov method to construct the source function f(x) of the parabolic diffusion equation. This problem is well known to be severely illā€posed. Therefore, regularization is required. The error estimates between the sought solution and the regularized solution are obtained under an a priori parameter choice rule and an a posteriori parameter choice rule, respectively. One numerical test illustrates that the proposed method is feasible and effective.

Keywords: parabolic equation; term parabolic; recovering source; equation; source; source term

Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2021

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