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Séminaire du LJLL - 22 06 2018 14h00 : H. Matano
Hiroshi Matano (Université Meiji, Tokyo)
Stability of fronts in a bidomain model
Résumé
Bidomain models are important mathematical models for describing electro-physiological activities in the heart. While the classical Hodgkin-Huxley model and the FitzHugh-Nagumo model are based on diffusion equations, bidomain models, on the other hand, are formulated as nonlocal pseudo-differential equations. It is known that bidomain models can simulate cardiac electro-physiological activities more accurately than the classical diffusion models.
In this talk, I will focus on the bidomain Allen-Cahn model and study the properties of propagating fronts. First I will review my earlier work with Yoichiro Mori on the linear (spectral) stability of planar fronts on R^2. Then I will discuss the nonlinear stability of front solutions of the bidomain Allen-Cahn model in an infinite strip. I will also talk about bifurcation phenomena of the front solution.
This is joint work with Yoichiro Mori and Mitsunori Nara.