Some remarks on spatial uniformity of solutions of reaction-diffusion PDE's and a related synchronization problem for ODE's
Systems and Control
2014-09-22 v4 Analysis of PDEs
Abstract
In this note, we present a condition which guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction-diffusion PDE with Neumann boundary conditions in one dimension, using the Jacobian matrix of the reaction term and the first Dirichlet eigenvalue of the Laplacian operator on the given spatial domain. We also derive an analog of this PDE result for the synchronization of a network of identical ODE models coupled by diffusion terms.
Keywords
Cite
@article{arxiv.1312.7145,
title = {Some remarks on spatial uniformity of solutions of reaction-diffusion PDE's and a related synchronization problem for ODE's},
author = {Zahra Aminzare and Eduardo D. Sontag},
journal= {arXiv preprint arXiv:1312.7145},
year = {2014}
}
Comments
arXiv admin note: text overlap with arXiv:1208.0326