Universidad Complutense de Madrid
E-Prints Complutense

Wave solutions for a discrete reaction-diffusion equation

Impacto

Descargas

Último año

Carpio, Ana y Chapman, S.J. y Hastings, S. y Mcleod, J.B. (2000) Wave solutions for a discrete reaction-diffusion equation. European Journal of Applied Mathematics, 11 (4). pp. 399-412. ISSN 0956-7925

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 2020.

259kB

URL Oficial: http://journals.cambridge.org/abstract_S0956792599004222


URLTipo de URL
http://www.cambridge.org/Editorial


Resumen

Motivated by models from fracture mechanics and from biology, we study the infinite system of differential equations u'(n) = u(n-1) - 2u(n) + u(n+1) - A sin u(n) + F, ' = d/dt, where A and F are positive parameters. For fixed A > 0 we show that there are monotone travelling waves for F in an interval F-crit < F < A, and we are able to give a rigorous upper bound for F-crit, in contrast to previous work on similar problems. We raise the problem of characterizing those nonlinearities (apparently the more common) for which F-crit > 0. We show that, for the sine nonlinearity, this is true if A > 2. (Our method yields better estimates than this, but does not include all A > 0.) We also consider the existence and multiplicity of time independent solutions when \F\ < F-crit.


Tipo de documento:Artículo
Palabras clave:Nagumo equation; Systems; Propagation
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:15100
Depositado:04 May 2012 11:49
Última Modificación:28 Oct 2016 08:33

Descargas en el último año

Sólo personal del repositorio: página de control del artículo