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

Details Existence, uniqueness and a priori estimates for a non linear integro-differential equation Existence, uniqueness and a priori estimates for a non linear integro-differential equation

2012-03-02

arxiv.org/abs/1203.0441v1

Ricerche mat. 57 p. 95-109 (2008)

Physics

Mathematical Physics

Scientific paper

10.1007/S11587(08)0028-7

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.

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