Open AccessA Cauchy problem for the asymmetric Parabolic equation in polar coordinates with the perturbed diffusivity
Author(s) -
Tran Hoai Nhan,
Ho Hoang Yen,
Luu Hong Phong
Publication year - 2019
Publication title -
tạp chí khoa học đại học sư phạm thành phố hồ chí minh
Language(s) - English
Resource type - Journals
ISSN - 2734-9918
DOI - 10.54607/hcmue.js.16.3.2455(2019
Subject(s) - polar coordinate system , bessel function , parabolic cylindrical coordinates , mathematical analysis , cartesian coordinate system , mathematics , thermal diffusivity , heat equation , curvilinear coordinates , parabolic partial differential equation , boundary value problem , cylindrical coordinate system , spherical coordinate system , generalized coordinates , inverse problem , log polar coordinates , partial differential equation , geometry , physics , parabolic cylinder function , thermodynamics
The inverse problem for the heat equation plays an important area of study and application. Up to now, the backward heat problem (BHP) in Cartesian coordinates has been arisen in many articles, but the BHP in different domains such as polar coordinates, cylindrical one or spherical one is rarely considered. This paper’s purpose is to investigate the BHP on a disk, especially, the problem is associated with the perturbed diffusivity and the space-dependent heat source. In order to solve the problem, the authors apply the separation of variables method, associated with the Bessel’s equation and Bessel’s expansion. Based on the exact solution, the regularized solution is constructed by using the modified quasi-boundary value method. As a result, a Holder type of convergence rate has been obtained. In addition, a numerical experiment is given to illustrate the flexibility and effectiveness of the used method.