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.
Existence, uniqueness and a priori estimates for a nonlinear integro-differential equation / DE ANGELIS, Monica; Renno, Pasquale. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - STAMPA. - 57 (1):(2008), pp. 95-109. [10.1007/s11587-008-0028-7]
Existence, uniqueness and a priori estimates for a nonlinear integro-differential equation
DE ANGELIS, MONICA
;RENNO, PASQUALE
2008
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.File | Dimensione | Formato | |
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