Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The asymptotic behaviour of the heat equation in a twisted
  Dirichlet-Neumann waveguide   We consider the heat equation in a straight strip, subject to a combination
of Dirichlet and Neumann boundary conditions. We show that a switch of the
respective boundary conditions leads to an improvement of the decay rate of the
heat semigroup of the order of $t^{-1/2}$. The proof employs similarity
variables that lead to a non-autonomous parabolic equation in a thin strip
contracting to the real line, that can be analyzed on weighted Sobolev spaces
in which the operators under consideration have discrete spectra. A careful
analysis of its asymptotic behaviour shows that an added Dirichlet boundary
condition emerges asymptotically at the switching point, breaking the real line
in two half-lines, which leads asymptotically to the 1/2 gain on the spectral
lower bound, and the $t^{-1/2}$ gain on the decay rate in the original physical
variables.
  This result is an adaptation to the case of strips with twisted boundary
conditions of previous results by the authors on geometrically twisted
Dirichlet tubes.

32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
19
The categories of this paper are: eess