Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal and minimal spreading speeds for reaction diffusion equations in
  nonperiodic slowly varying media   This paper investigates the asymptotic behavior of the solutions of the
Fisher-KPP equation in a heterogeneous medium, $$\partial_t u = \partial_{xx} u
+ f(x,u),$$ associated with a compactly supported initial datum. A typical
nonlinearity we consider is $f(x,u) = \mu_0 (\phi (x)) u(1-u)$, where $\mu_0$
is a 1-periodic function and $\phi$ is a $\mathcal{C}^1$ increasing function
that satisfies $\lim_{x\to +\infty} \phi (x) = +\infty$ and $\lim_{x\to
+\infty} \phi' (x) = 0$. Although quite specific, the choice of such a reaction
term is motivated by its highly heterogeneous nature. We exhibit two different
behaviors for $u$ for large times, depending on the speed of the convergence of
$\phi$ at infinity. If $\phi$ grows sufficiently slowly, then we prove that the
spreading speed of $u$ oscillates between two distinct values. If $\phi$ grows
rapidly, then we compute explicitly a unique and well determined speed of
propagation $w_\infty$, arising from the limiting problem of an infinite
period. We give a heuristic interpretation for these two behaviors.

15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin