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arXiv · 1203.0441

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

M. De Angelis·P. Renno
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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.

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BibTeXRIS

M. De Angelis, P. Renno. 2012-03-02. Existence, uniqueness and a priori estimates for a non linear integro-differential equation. https://doi.org/10.1007/s11587(08)0028-7

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