Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large time behavior of solutions of Trudinger's equation   We study the large time behavior of solutions
$v:\Omega\times(0,\infty)\rightarrow \mathbb{R}$ of the PDE
$\partial_t(|v|^{p-2}v)=\Delta_pv.$ We show that
$e^{\left(\lambda_p/(p-1)\right)t}v(x,t)$ converges to an extremal of a
Poincar\'e inequality on $\Omega$ with optimal constant $\lambda_p$, as
$t\rightarrow \infty$. We also prove that the large time values of solutions
approximate the extremals of a corresponding "dual" Poincar\'e inequality on
$\Omega$. Moreover, our theory allows us to deduce the large time asymptotics
of related doubly nonlinear flows involving various boundary conditions and
nonlocal operators.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn