Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transitions for nonlinear nonlocal aggregation-diffusion equations   We are interested in studying the stationary solutions and phase transitions
of aggregation equations with degenerate diffusion of porous medium-type, with
exponent $1 < m < \infty$. We first prove the existence of possibly infinitely
many bifurcations from the spatially homogeneous steady state. We then focus
our attention on the associated free energy proving existence of minimisers and
even uniqueness for sufficiently weak interactions. In the absence of
uniqueness, we show that the system exhibits phase transitions: we classify
values of $m$ and interaction potentials $W$ for which these phase transitions
are continuous or discontinuous. Finally, we comment on the limit $m \to
\infty$ and the influence that the presence of a phase transition has on this
limit.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs