A Neumann problem in the strip for the Fitzhugh Nagumo system is considered. The transformation in a non linear integral equation permits to deduce a priori estimates for the solution. A complete asymptotic analysis shows that for large t the eects of the initial data vanish while the eects of boundary disturbances '1(t); '2(t) depend on the properties of the data. When '1; '2 are convergent for large t, the solution is everywhere bounded and depends on the asymptotic values of '1; '2. More, when 'i 2 L1(0;1)(i = 1; 2) too, the eects are vanishing.
ASYMPTOTIC EFFECTS OF BOUNDARY PERTURBATIONS IN EXCITABLE SYSTEMS / DE ANGELIS, Monica; Renno, Pasquale. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - 19:7(2014), pp. 2039-2045. [10.3934/dcdsb.2014.19.2039]
ASYMPTOTIC EFFECTS OF BOUNDARY PERTURBATIONS IN EXCITABLE SYSTEMS
DE ANGELIS, MONICA;RENNO, PASQUALE
2014
Abstract
A Neumann problem in the strip for the Fitzhugh Nagumo system is considered. The transformation in a non linear integral equation permits to deduce a priori estimates for the solution. A complete asymptotic analysis shows that for large t the eects of the initial data vanish while the eects of boundary disturbances '1(t); '2(t) depend on the properties of the data. When '1; '2 are convergent for large t, the solution is everywhere bounded and depends on the asymptotic values of '1; '2. More, when 'i 2 L1(0;1)(i = 1; 2) too, the eects are vanishing.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
