Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the convergence of stationary solutions in the Smoluchowski-Kramers
  approximation of infinite dimensional systems   We prove the convergence, in the small mass limit, of statistically invariant
states for a class of semi-linear damped wave equations, perturbed by an
additive Gaussian noise, both with Lipschitz-continuous and with polynomial
non-linearities. In particular, we prove that the first marginals of any
sequence of invariant measures for the stochastic wave equation converge in a
suitable Wasserstein metric to the unique invariant measure of the limiting
stochastic semi-linear parabolic equation obtained in the Smoluchowski-Kramers
approximation. The Wasserstein metric is associated to a suitable distance on
the space of square integrable functions, that is chosen in such a way that the
dynamics of the limiting stochastic parabolic equation is contractive with
respect to such a Wasserstein metric. This implies that the limiting result is
a consequence of the validity of a generalized Smoluchowski-Kramers limit at
fixed times. The proof of such a generalized limit requires new delicate bounds
for the solutions of the stochastic wave equation, that must be uniform with
respect to the size of the mass.

36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin