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Resumo(s)
We study some properties of the monotone solutions of the boundary value problem
(p(u'))' - cu' + f(u) = 0,
u(-infinity) = 0, u(+infinity) = 1,
where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2).
The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered.
We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.
Descrição
Palavras-chave
Relativistic Curvature p-Laplacian FKPP Equation Heteroclinic Travelling Wave Critical Speed
Contexto Educativo
Citação
COELHO, Maria Isabel Esteves; SANCHEZ, Luís – Travelling wave profiles in some models with nonlinear diffusion. Applied Mathematics and Computation. ISSN: 0096-3003. Vol. 235 (2014), pp. 469-481
Editora
Elsevier Science Inc