Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variational approach to reaction diffusion equations with forced speed
  in dimension 1   We investigate in this paper a scalar reaction diffusion equation with a
nonlinear reaction term depending on x-ct. Here, c is a prescribed parameter
modelling the speed of climate change and we wonder whether a population will
survive or not, that is, we want to determine the large-time behaviour of the
associated solution. This problem has been solved recently when the
nonlinearity is of KPP type. We consider in the present paper general reaction
terms, that are only assumed to be negative at infinity. Using a variational
approach, we construct two thresholds determining the existence and the
non-existence of travelling waves. Numerics support the conjecture that the two
thresholds are equal. We then prove that any solution of the initial-value
problem converges at large times, either to 0 or to a travelling wave. In the
case of bistable nonlinearities, where the steady state 0 is assumed to be
stable, our results lead to constrasting phenomena with respect to the KPP
framework. Lastly, we illustrate our results and discuss several open questions
through numerics.

19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol