Coelho, Maria Isabel EstevesSanchez, Luis2015-08-252015-08-252014-05-25COELHO, 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. 469-4810096-30031873-5649http://hdl.handle.net/10400.21/5018We 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.engRelativistic Curvaturep-LaplacianFKPP EquationHeteroclinicTravelling WaveCritical Speedjournal article10.1016/j.amc.2014.02.104