Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transfers of energy through fast diffusion channels in some resonant
  PDEs on the circle   In this paper we consider two classes of resonant Hamiltonian PDEs on the
circle with non-convex (respect to actions) first order resonant Hamiltonian.
We show that, for appropriate choices of the nonlinearities we can find
time-independent linear potentials that enable the construction of solutions
that undergo a prescribed growth in the Sobolev norms. The solutions that we
provide follow closely the orbits of a nonlinear resonant model, which is a
good approximation of the full equation. The non-convexity of the resonant
Hamiltonian allows the existence of fast diffusion channels along which the
orbits of the resonant model experience a large drift in the actions in the
optimal time. This phenomenon induces a transfer of energy among the Fourier
modes of the solutions which in turn is responsible for the growth of higher
order Sobolev norms.

15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex