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Singular Limits of Reaction Diffusion Equations of Kpp Type in an Infinite Cylinder.
by
Fernando Carreon
Arizona State University
The limit of a scaled reaction diffusion equation of KPP type on an infinite cylinder is analyzed using viscosity solution methods. The reaction term of this equation has two equilibrium states, one stable and the other unstable. The equation is scaled with two small parameters. We show that the solutions of the scaled equation converge locally uniformly to piecewise constant function that attains the equilibrium of the equation, as the parameters approach zero. The regions where the solutions converge to each equilibrium state are characterized through the viscosity solution of a variational inequality. The coefficients of the variational inequality are obtained using concepts from homogenization of elliptic operators.
Date received: August 28, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cauf-53.