Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow up profiles for a quasilinear reaction-diffusion equation with
  weighted reaction   We perform a thorough study of the blow up profiles associated to the
following second order reaction-diffusion equation with non-homogeneous
reaction: $$ \partial_tu=\partial_{xx}(u^m) + |x|^{\sigma}u^p, $$ in the range
of exponents $1<p<m$ and $\sigma>0$. We classify blow up solutions in
self-similar form, that are likely to represent typical blow up patterns for
general solutions. We thus show that the non-homogeneous coefficient
$|x|^{\sigma}$ has a strong influence on the qualitative aspects related to the
finite time blow up. More precisely, for $\sigma\sim0$, blow up profiles have
similar behavior to the well-established profiles for the homogeneous case
$\sigma=0$, and typically \emph{global blow up} occurs, while for $\sigma>0$
sufficiently large, there exist blow up profiles for which blow up \emph{occurs
only at space infinity}, in strong contrast with the homogeneous case. This
work is a part of a larger program of understanding the influence of unbounded
weights on the blow up behavior for reaction-diffusion equations.

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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat