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

Source: [Existence, uniqueness and a priori estimates for a non linear integro-differential equation](<https://www.sota2.com/research/paper/68fa2b1d1e209131ce844033>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T14:00:18.558Z

Authors: M.De Angelis, P. Renno

Published: 2012-03-02T12:22:12.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1203.0441>)

[PDF](<https://arxiv.org/pdf/1203.0441.pdf>)