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Nonlinear evolution equations with exponential nonlinearities: conditional symmetries and exact solutions

Roman Cherniha, Oleksii Pliukhin (2011)

Banach Center Publications

New Q-conditional symmetries for a class of reaction-diffusion-convection equations with exponential diffusivities are derived. It is shown that the known results for reaction-diffusion equations with exponential diffusivities follow as particular cases from those obtained here but not vice versa. The symmetries obtained are applied to construct exact solutions of the relevant nonlinear equations. An application of exact solutions to solving a boundary-value problem with constant Dirichlet conditions...

Numerical study of the stopping of aura during migraine

C. Pocci, A. Moussa, F. Hubert, G. Chapuisat (2010)

ESAIM: Proceedings

This work is devoted to the study of migraine with aura in the human brain. Following [6], we class migraine as a propagation of a wave of depolarization through the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly presented. The equation is considered in a duct containing a bend, in order to model one of the numerous circumvolutions of the brain. For a wide set of parameters, one can establish the existence...

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