An asymmetric backward problem for the inhomogeneous parabolic equation with time-dependent diffusivity

In this paper, we deal with an asymmetric case of the non-homogeneous backward parabolic problem associated with time-dependent diffusivity in polar coordinates which arises in describing the heat transfer in cylinder. In general, this problem is severely ill-posed by the Hadamard instability. To su...

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Bibliographic Details
Published in:Computational & applied mathematics 2018-07, Vol.37 (3), p.3241-3255
Main Authors: Le Minh, Triet, Hong, Phong Luu, Hoang, Quan Pham
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Boundary value problems
Computational mathematics
Computational Mathematics and Numerical Analysis
Cylinders
Diffusivity
Ill posed problems
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Polar coordinates
Stability
Time dependence
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Summary:In this paper, we deal with an asymmetric case of the non-homogeneous backward parabolic problem associated with time-dependent diffusivity in polar coordinates which arises in describing the heat transfer in cylinder. In general, this problem is severely ill-posed by the Hadamard instability. To subdue the instability of this problem, we apply the modified quasi-boundary value method. According to some a priori assumptions on the exact solution, we get an explicit error estimate of Hölder type for all t ∈ ( 0 , T ] . In addition, a numerical experiment is given to illustrate the efficiency and flexibility of our method.
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-017-0509-y