Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behaviour of solutions of the fast diffusion equation near
  its extinction time   Let $n\ge 3$, $0<m<\frac{n-2}{n}$, $\rho_1>0$,
$\beta\ge\frac{m\rho_1}{n-2-nm}$ and $\alpha=\frac{2\beta+\rho_1}{1-m}$. For
any $\lambda>0$, we will prove the existence and uniqueness (for
$\beta\ge\frac{\rho_1}{n-2-nm}$) of radially symmetric singular solution
$g_{\lambda}\in C^{\infty}(R^n\setminus\{0\})$ of the elliptic equation $\Delta
v^m+\alpha v+\beta x\cdot\nabla v=0$, $v>0$, in $R^n\setminus\{0\}$, satisfying
$\displaystyle\lim_{|x|\to
0}|x|^{\alpha/\beta}g_{\lambda}(x)=\lambda^{-\frac{\rho_1}{(1-m)\beta}}$. When
$\beta$ is sufficiently large, we prove the higher order asymptotic behaviour
of radially symmetric solutions of the above elliptic equation as
$|x|\to\infty$. We also obtain an inversion formula for the radially symmetric
solution of the above equation. As a consequence we will prove the extinction
behaviour of the solution $u$ of the fast diffusion equation $u_t=\Delta u^m$
in $R^n\times (0,T)$ near the extinction time $T>0$.

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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph