1203.0441 (M. De Angelis et al.)

Existence, uniqueness and a priori estimates for a non linear
integro-differential equation    [PDF]

M. De Angelis, P. Renno

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.

View original: http://arxiv.org/abs/1203.0441