Title: The remarkable simple and universal properties of "pulled" fronts propagating into an unstable state
Speaker: Professor W. van Saarloos
Speaker Info: U. Leyden, Netherlands
Brief Description:
Special Note:
Abstract:
In this talk, we will discuss fronts which propagate into a linearly unstable state. We will focus in particular on so-called pulled fronts, fronts whose asymptotic propagation velocity is equal to the asymptotic velocity with which an initial condition grows and spreads according to the equations, linearized into an unstable state. The simplest example of this occurs in the nonlinear diffusion equation analyzed over 60 years ago by Fisher and by Kolmogorov et al., but the same dynamics occurs in many different classes of equations, higher order p.d.e.'s and sets of coupled p.d.e.'s, difference-differential equations, or integro-differential equations. We will discuss new exact results for the asymptotic rate of convergence of the velocity of pulled fronts to their asymptotic value. These results are universal, in that they are independent of the precise form of the dynamical equation, including the nonlinearities. Some of the results can even be generalized to pattern forming or chaotic fronts, such as those which occur in the Swift-Hohenberg equation or Complex Ginzburg Landau equation.Date: Friday, March 17, 2000