Determine the special term of a two-dimensional heat source

Authors: Trong, Dang Duc¹; Dinh Alain, Pham Ngoc²; Thanh Nam, Phan¹

Source: Applicable Analysis, Volume 88, Number 3, March 2009 , pp. 457-474(18)

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Abstract:

We consider the problem of determining a pair of functions (u, f) satisfying the heat equation [image omitted], where [image omitted] and the function Φ is given. The problem is ill-posed. Under a slight condition on Φ, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier series, we construct a regularized solution of the source term f from non-smooth data. The error estimate and numerical experiments are given.

Keywords: heat source; ill-posed problem; interpolation method; Fourier series

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00036810902889534

Affiliations: 1: Mathematics Department, HoChiMinh City National University, HoChiMinh City, Viet Nam 2: Mathematics Department, Orleans Cedex, France

Publication date: 2009-03-01

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