Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a doubly nonlinear diffusion model of chemotaxis with prevention of
  overcrowding   This paper addresses the existence and regularity of weak solutions for a
fully parabolic model of chemotaxis, with prevention of overcrowding, that
degenerates in a two-sided fashion, including an extra nonlinearity represented
by a $p$-Laplacian diffusion term. To prove the existence of weak solutions, a
Schauder fixed-point argument is applied to a regularized problem and the
compactness method is used to pass to the limit. The local H\"older regularity
of weak solutions is established using the method of intrinsic scaling. The
results are a contribution to showing, qualitatively, to what extent the
properties of the classical Keller-Segel chemotaxis models are preserved in a
more general setting. Some numerical examples illustrate the model.

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
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an