Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse problem of reconstruction of degenerate diffusion coefficient in
  a parabolic equation   We consider the inverse problem of identification of degenerate diffusion
coefficient of the form $x^\alpha a(x)$ in a one dimensional parabolic equation
by some extra data. We first prove by energy methods the uniqueness and
Lipschitz stability results for the identification of a constant coefficient
$a$ and the power $\alpha$ by knowing an interior data at some time.
  On the other hand, we obtain the uniqueness result for the identification of
a general diffusion coefficients $a(x)$ and also the power $\alpha$ form a
boundary data on one side of the space interval. The proof is based on global
Carleman estimates for a hyperbolic problem and an inversion of the integral
transform similar to the Laplace transform. Finally, the theoretical results
are satisfactory verified by numerically experiments.

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The categories of this paper are: eess
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The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph