Determine the source term of a two-dimensional heat equation

Details Determine the source term of a two-dimensional heat equation Determine the source term of a two-dimensional heat equation

2008-07-11

arxiv.org/abs/0807.1812v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a specific form of Fourier transforms, we shall show that the heat source is determined uniquely by the minimum boundary condition and the temperature distribution in $\Omega$ at the initial time $t=0$ and at the final time $t=1$. Using the methods of Tikhonov's regularization and truncated integration, we construct the regularized solutions. Numerical part is given.

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