Abstract
We are interested in the existence of depolarization waves in the human brain. These waves propagate in the grey matter and are absorbed in the white matter. We consider a two-dimensional model ut = Δ u + f(u)𝟙|y|≤R − αu𝟙|y|>R, with f a bistable nonlinearity taking effect only on the domain ℝ × [−R, R], which represents the grey matter layer. We study the existence, the stability and the energy of nontrivial asymptotic profiles of the possible traveling fronts. For this purpose, we present dynamical systems techniques and graphic criteria based on Sturm–Liouville theory and apply them to the above equation. This yields three different types of behavior for the solution u after stimulation, depending on the thickness R of the grey matter. This may partly explain the difficulties to observe depolarization waves in the human brain.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Mathematical Models and Methods in Applied Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
