RT Journal Article
T1 Wave solutions for a discrete reaction-diffusion equation
A1 Carpio Rodríguez, Ana María
A1 Chapman, S. J.
A1 Hastings, S.
A1 Mcleod, J. B.
AB 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.
PB Cambridge University Press
SN 0956-7925
YR 2000
FD 2000
LK https://hdl.handle.net/20.500.14352/57218
UL https://hdl.handle.net/20.500.14352/57218
LA eng
NO Carpio Rodríguez, A. M., Chapman, S. J., Hastings, S. & Mcleod, J. B. «Wave Solutions for a Discrete Reaction-Diffusion Equation». European Journal of Applied Mathematics, vol. 11, n.o 4, septiembre de 2000, pp. 399-412. DOI.org (Crossref), https://doi.org/10.1017/S0956792599004222.
DS Docta Complutense
RD 12 abr 2025