A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities

Simon Eberle

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arXiv · 1706.04092

A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities

Simon Eberle

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Abstract

In this paper we consider a semilinear parabolic equation in an infinite cylinder. The spatially varying nonlinearity is such that it connects two (spatially independent) bistable nonlinearities in a compact set in space. We prove that, given such a setting, a traveling wave obeying the equation with the one bistable nonlinearity and starting at the respective side of the cylinder, will converge to a traveling wave solution prescribed by the nonlinearity on the other side.

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Simon Eberle. 2017-06-13. A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities. https://arxiv.org/abs/1706.04092

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