Multiplicity of supercritical fronts for reaction-diffusion equations in cylinders

P. V. Gordon; C. B. Muratov; M. Novaga

doi:10.1007/s00526-012-0532-1

Multiplicity of supercritical fronts for reaction-diffusion equations in cylinders

P. V. Gordon, C. B. Muratov, M. Novaga

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion 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, in fact, 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.

Original language	English (US)
Pages (from-to)	683-709
Number of pages	27
Journal	Calculus of Variations and Partial Differential Equations
Volume	47
Issue number	3-4
DOIs	https://doi.org/10.1007/s00526-012-0532-1
State	Published - Jul 2013

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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abstract = "We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion 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, in fact, 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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AU - Gordon, P. V.

AU - Muratov, C. B.

AU - Novaga, M.

PY - 2013/7

Y1 - 2013/7

N2 - We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion 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, in fact, 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.

AB - We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion 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, in fact, 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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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

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ER -

Multiplicity of supercritical fronts for reaction-diffusion equations in cylinders

Abstract

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