Article ID Journal Published Year Pages File Type
4627852 Applied Mathematics and Computation 2014 13 Pages PDF
Abstract

We study some properties of the monotone solutions of the boundary value problem(P(u′))′-cu′+f(u)=0,u(-∞)=0,u(+∞)=1,where f   is a continuous function, positive in (0,1)(0,1) and taking the value zero at 0 and 1, and P   may be an increasing homeomorphism of [0,1)[0,1) or [0,+∞)[0,+∞) onto [0,+∞)[0,+∞). This problem arises when we look for travelling waves for the reaction diffusion equation∂u∂t=∂∂xP∂u∂x+f(u)with the parameter c representing the wave speed.A possible model for the nonlinear diffusion is the relativistic curvature operator P(v)=v1-v2.The same ideas apply when P is given by the one-dimensional p  -Laplacian P(v)=|v|p-2vP(v)=vp-2v. 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∗,+∞)[c∗,+∞) and we give characterisations of the critical speed c∗c∗. We also present some examples of exact solutions.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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