%0 Journal Article
%T Existence, uniqueness and a priori estimates for a non linear integro-differential equation
%A M. De Angelis
%A P. Renno
%J Quantitative Biology
%D 2012
%I arXiv
%R 10.1007/S11587(08)0028-7
%X 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.
%U http://arxiv.org/abs/1203.0441v1