Analysis for two-dimensional inverse quasilinear parabolic problem by Fourier method. Issue 12 (2nd December 2021)

• Record Type: Journal Article
• Authors: Kanca, Fatma; Baglan, Irem
• Is Part Of: Inverse problems in science and engineering. Volume 29:Issue 12(2021)
• Page Start: 1912
• Page End: 1945
• Publication Date: 2021-12-02
• Subjects: Inverse problem -- two-dimensional heat problem -- periodic boundary conditions; 35K55 -- 35K70; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2021.1890068
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : In this work, two-dimensional inverse quasi-linear parabolic problem with periodic boundary and integral overdetermination conditions is investigated. The formal solution is obtained by the Fourier approximation. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness and continuously dependence upon the data of the solution are proved by iteration method. The inverse problem is first examined by linearization and then used implicit finite difference scheme for the numerical solution. Also predictor corrector method is considered in the numerical approach. Some results on the numerical solution with two examples are presented with figures and tables. The sensitivity of the scheme with respect to noisy overdetermination data is illustrated.