The evolution to localized and front solutions in a non-Lipschitz reaction-diffusion Cauchy problem with trivial initial data

28 Jul 2016  ·  Meyer John Christopher, Needham David John ·

In this paper, we establish the existence of spatially inhomogeneous classical self-similar solutions to a non-Lipschitz semi-linear parabolic Cauchy problem with trivial initial data. Specifically we consider bounded solutions to an associated two-dimensional non-Lipschitz non-autonomous dynamical system, for which, we establish the existence of a two-parameter family of homoclinic connections on the origin, and a heteroclinic connection between two equilibrium points... Additionally, we obtain bounds and estimates on the rate of convergence of the homoclinic connections to the origin. read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Analysis of PDEs Classical Analysis and ODEs