Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determine the source term of a two-dimensional heat equation   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.

27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex