Existence, uniqueness and a priori estimates for a non linear integro-differential equation
Mathematical Physics
2012-03-05 v1 Disordered Systems and Neural Networks
Superconductivity
math.MP
Neurons and Cognition
Abstract
The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem in all of the space is analyzed together with continuous dependence and a priori estimates of the solution. These estimates show that the asymptotic behavior is determined by the reaction mechanism. Moreover it's possible a rigorous singular perturbation analysis for discussing travelling waves with their characteristic times.
Cite
@article{arxiv.1203.0441,
title = {Existence, uniqueness and a priori estimates for a non linear integro-differential equation},
author = {M. De Angelis and P. Renno},
journal= {arXiv preprint arXiv:1203.0441},
year = {2012}
}