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 traveling
  waves for spatially periodic KPP type equations   We consider a variational problem associated with the minimal speed of
pulsating traveling waves of the equation $u_t=u_{xx}+b(x)(1-u)u$,
$x\in{\mathbb R},\ t>0$, where the coefficient $b(x)$ is nonnegative and
periodic in $x\in{\mathbb R}$ with a period $L>0$. It is known that there
exists a quantity $c^*(b)>0$ such that a pulsating traveling wave with the
average speed $c>0$ exists if and only if $c\geq c^*(b)$. The quantity $c^*(b)$
is the so-called minimal speed of pulsating traveling waves. In this paper, we
study the problem of maximizing $c^*(b)$ by varying the coefficient $b(x)$
under some constraints. We prove the existence of the maximizer under a certain
assumption of the constraint and derive the Euler--Lagrange equation which the
maximizer satisfies under $L^2$ constraint $\int_0^L b(x)^2dx=\beta$. The limit
problems of the solution of this Euler--Lagrange equation as $L\rightarrow0$
and as $\beta\rightarrow0$ are also considered. Moreover, we also consider the
variational problem in a certain class of step functions under $L^p$ constraint
$\int_0^L b(x)^pdx=\beta$ when $L$ or $\beta$ tends to infinity.

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an