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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...
In this paper we study a linear population dynamics model. In this model, the birth process is described by a nonlocal term and the initial distribution is unknown. The aim of this paper is to use a controllability result of the adjoint system for the computation of the density of individuals at some time .
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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