Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the self-similar asymptotics for generalized non-linear kinetic
  Maxwell models   Maxwell models for nonlinear kinetic equations have many applications in
physics, dynamics of granular gases, economy, etc. In the present manuscript we
consider such models from a very general point of view, including those with
arbitrary polynomial non-linearities and in any dimension space. It is shown
that the whole class of generalized Maxwell models satisfies properties which
one of them can be interpreted as an operator generalization of usual Lipschitz
conditions. This property allows to describe in detail a behavior of solutions
to the corresponding initial value problem. In particular, we prove in the most
general case an existence of self similar solutions and study the convergence,
in the sense of probability measures, of dynamically scaled solutions to the
Cauchy problem to those self-similar solutions, as time goes to infinity. The
properties of these self-similar solutions, leading to non classical
equilibrium stable states, are studied in detail. We apply the results to three
different specific problems related to the Boltzmann equation (with elastic and
inelastic interactions) and show that all physically relevant properties of
solutions follow directly from the general theory developed in this paper.

35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th