Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Single-point blow-up for parabolic systems with exponential
  nonlinearities and unequal diffusivities   We study positive blowing-up solutions of systems of the form: $$u_t=\delta_1
\Delta u+e^{pv},\quad v_t= \delta_2\Delta v+e^{qu},$$ with
$\delta_1,\delta_2>0$ and $p, q>0$. We prove single-point blow-up for large
classes of radially decreasing solutions. This answers a question left open in
a paper of Friedman and Giga~(1987), where the result was obtained only for the
equidiffusive case $\delta_1=\delta_2$ and the proof depended crucially on this
assumption.

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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph