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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This work has been performed under the auspices of the G.N.F.M. of I.N.D.A.M. and M.I.U.R. (P.R.I.N. 2007) “Waves and stability in continuous media”.
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De Angelis, M., Renno, P. Existence, uniqueness and a priori estimates for a nonlinear integro-differential equation. Ricerche mat. 57, 95–109 (2008). https://doi.org/10.1007/s11587-008-0028-7
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DOI: https://doi.org/10.1007/s11587-008-0028-7
Keywords
- Reaction–diffusion systems
- Parabolic equations
- Biological applications
- Fundamental solutions
- Laplace transform