Analysis for two-dimensional inverse quasilinear parabolic problem by Fourier method

Kanca F., BAĞLAN İ.

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, cilt.29, sa.12, ss.1912-1945, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 12
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/17415977.2021.1890068
  • Dergi Adı: INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1912-1945
  • Anahtar Kelimeler: Inverse problem, two-dimensional heat problem, periodic boundary conditions, ALGORITHM, EQUATION
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.