Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contracting differential equations in weighted Banach spaces   Geodesic contraction in vector-valued differential equations is readily
verified by linearized operators which are uniformly negative-definite in the
Riemannian metric. In the infinite-dimensional setting, however, such analysis
is generally restricted to norm-contracting systems. We develop a
generalization of geodesic contraction rates to Banach spaces using a
smoothly-weighted semi-inner product structure on tangent spaces. We show that
negative contraction rates in bijectively weighted spaces imply asymptotic
norm-contraction, and apply recent results on asymptotic contractions in Banach
spaces to establish the existence of fixed points. We then show that
contraction in surjectively weighted spaces verify non-equilibrium asymptotic
properties, such as convergence to finite- and infinite-dimensional subspaces,
submanifolds, limit cycles, and phase-locking phenomena. We use contraction
rates in weighted Sobolev spaces to establish existence and continuous data
dependence in nonlinear PDEs, and pose a method for constructing weak solutions
using vanishing dissipative approximations. We discuss applications to control
and order reduction of distributed systems.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg