Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse Problem of Finding the Coefficient of the Lowest Term in
  Two-dimensional Heat Equation with Ionkin-type Boundary Condition   We consider an inverse problem of determining the time-dependent lowest order
coefficient of two-dimensional (2D) heat equation with Ionkin boundary and
total energy integral overdetermination condition. The well-posedness of the
problem is obtained by generalized Fourier method combined by the Banach fixed
poind theorem. For obtaining a numerical solution of the inverse problem, we
propose the discretization method from a new combination. On the one hand, it
is known the traditional method of uniform finite difference combined with
numerical integration on a uniform grid (trapezoidal and Simpson's), on the
other hand, we give the method of non-uniform finite difference is combined by
a numerical integration on a non-uniform grid (with Gauss-Lobatto nodes).
Numerical examples illustrate how to implement the method.

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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys