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
modified on 10 Nov 2018


Published Paper

Inserted: 8 dec 2011
Last Updated: 10 nov 2018

Journal: Calc. Var. PDE
Volume: 47
Number: 3-4
Pages: 683-709
Year: 2013


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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