Inserted: 5 may 2003
Last Updated: 4 apr 2016
Journal: Comm. Pure Appl. Math.
We revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction-diffusion equations with one linearly stable and one linearly unstable equilibrium. For a wide class of initial data this problem reduces to finding the minimal speed of the monotone traveling wave solutions connecting these two equilibria in one space dimension. We introduce a variational characterization of these traveling wave solutions and give a necessary and sufficient condition for linear vs. nonlinear selection mechanism. Easily verifiable sufficient conditions for the linear and nonlinear selection mechanisms are obtained. Our method also allows to obtain efficient lower and upper bounds for the propagation speed.