Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On an inverse problem in the parabolic equation arising from groundwater
  pollution problem   In this paper, we consider an inverse problem to determine a source term in a
parabolic equation, where the data are obtained at a certain time. In general,
this problem is ill-posed, therefore the Tikhonov regularization method is
proposed to solve the problem. In the theoretical results, a priori error
estimate between the exact solution and its regularized solutions is obtained.
We also propose both methods, a priori and a posteriori parameter choice rules.
In addition, the proposed methods have been verified by numerical experiments
to estimate the errors between the regularized solutions and exact solutions.
Eventually, from the numerical results it shows that the a posteriori parameter
choice rule method gives a better the convergence speed in comparison with the
a priori parameter choice rule method in some specific applications.

3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an