Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variational problem associated with the minimal speed of travelling
  waves for spatially periodic reaction-diffusion equations   We consider the equation $u_t=u_{xx}+b(x)u(1-u),$ $x\in\mathbb R,$ where
$b(x)$ is a nonnegative measure on $\mathbb R$ that is periodic in $x.$ In the
case where $b(x)$ is a smooth periodic function, it is known that there exists
a travelling wave with speed $c$ for any $c\geq c^*(b),$ where $c^*(b)$ is a
certain positive number depending on $b.$ Such a travelling wave is often
called a \lq\lq pulsating travelling wave" or a \lq\lq periodic travelling
wave", and $c^*(b)$ is called the \lq\lq minimal speed". In this paper, we
first extend this theory by showing the existence of the minimal speed $c^*(b)$
for any nonnegative measure $b$ with period $L.$ Next we study the question of
maximizing $c^*(b)$ under the constraint $\int_{[0,L)}b(x)dx=\alpha L,$ where
$\alpha$ is an arbitrarily given constant. This question is closely related to
the problem studied by mathematical ecologists in late 1980's but its answer
has not been known. We answer this question by proving that the maximum is
attained by periodically arrayed Dirac's delta functions $\alpha
L\sum_{k\in\mathbb Z}\delta(x+kL).$

9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th