Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eventual self-similarity of solutions for the diffusion equation with
  nonlinear absorption and a point source   This paper is concerned with the transient dynamics described by the
solutions of the reaction-diffusion equations in which the reaction term
consists of a combination of a superlinear power-law absorption and a
time-independent point source. In one space dimension, solutions of these
problems with zero initial data are known to approach the stationary solution
in an asymptotically self-similar manner. Here we show that this conclusion
remains true in two space dimensions, while in three and higher dimensions the
same conclusion holds true for all powers of the nonlinearity not exceeding the
Serrin critical exponent. The analysis requires dealing with solutions that
contain a persistent singularity and involves a variational proof of existence
of ultra-singular solutions, a special class of self-similar solutions in the
considered problem.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int