Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of a degenerate microscopic dynamics to the porous medium
  equation   We derive the porous medium equation from an interacting particle system
which belongs to the family of exclusion processes, with nearest neighbor
exchanges. The particles follow a degenerate dynamics, in the sense that the
jump rates can vanish for certain configurations, and there exist blocked
configurations that cannot evolve. In [Gon\c{c}alves-Landim-Toninelli '09] it
was proved that the macroscopic density profile in the hydrodynamic limit is
governed by the porous medium equation (PME), for initial densities uniformly
bounded away from $0$ and $1$. In this paper we consider the more general case
where the density can take those extreme values. In this context, the PME
solutions display a richer behavior, like moving interfaces, finite speed of
propagation and breaking of regularity. As a consequence, the standard
techniques that are commonly used to prove this hydrodynamic limits cannot be
straightforwardly applied to our case. We present here a way to generalize the
\emph{relative entropy method}, by involving approximations of solutions to the
hydrodynamic equation, instead of exact solutions.

20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol