Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The balance between diffusion and absorption in semilinear parabolic
  equations   Let $h:[0,\infty)\mapsto [0,\infty)$ be continuous and nondecreasing,
$h(t)>0$ if $t>0$, and $m,q$ be positive real numbers. We investigate the
behavior when $k\to\infty$ of the fundamental solutions $u=u_{k}$ of $\prt_{t}
u-\Delta u^m+h(t)u^q=0$ in $\Omega\ti (0,T)$ satisfying $u_{k}(x,0)=k\delta_0$.
The main question is wether the limit is still a solution of the above equation
with an isolated singularity at $(0,0)$, or a solution of the associated
ordinary differential equation $ u'+h(t)u^q=0$ which blows-up at $t=0$.

8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio