Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Blow-Up Problems for a Semilinear Parabolic Equation with a
  Potential   The blow-up rate estimate for the solution to a semilinear parabolic equation
$u_t=\Delta u+V(x) |u|^{p-1}u$ in $\Omega \times (0,T)$ with 0-Dirichlet
boundary condition is obtained. As an application, it is shown that the
asymptotic behavior of blow-up time and blow-up set of the problem with
nonnegative initial data $u(x,0)=M\vf (x)$ as $M$ goes to infinity, which have
been found in \cite{cer}, are improved under some reasonable and weaker
conditions compared with \cite{cer}.

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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph