Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On spatially uniform behavior in reaction-diffusion PDE and coupled ODE
  systems   We present a condition which guarantees spatial uniformity for the asymptotic
behavior of the solutions of a reaction-diffusion PDE with Neumann boundary
conditions. This condition makes use of the Jacobian matrix of the reaction
terms and the second Neumann eigenvalue of the Laplacian operator on the given
spatial domain, and replaces the global Lipschitz assumptions commonly used in
the literature with a less restrictive Lyapunov inequality. We then present
numerical procedures for the verification of this Lyapunov inequality and
illustrate them on models of several biochemical reaction networks. Finally, we
derive an analog of this PDE result for the synchronization of a network of
identical ODE models coupled by diffusion terms.

36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
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
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th