Calculus of Variations and Geometric Measure Theory
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P. Gordon - C. Muratov - M. Novaga

Multiplicity of supercritical fronts for reaction-diffusion equations in cylinders

created by novaga on 08 Dec 2011

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Submitted Paper

Inserted: 8 dec 2011
Last Updated: 8 dec 2011

Year: 2011

Abstract:

We study multiplicity of the supercritical traveling front solutions for scalar reaction-diff usion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions connecting an unstable equilibrium to the closest stable equilibrium for all speeds exceeding a critical value. We show that these are the only traveling front solutions in the considered problems for sufficiently large speeds. In addition, we show that other traveling fronts connecting to the unstable equilibrium may exist in a certain range of the wave speed. These results are obtained with the help of a variational characterization of such solutions.


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