臺灣大學數學系演講公告 博士生論文口試

Speaker：黃志強

Title：Travelling wave solutions of the diffusive FitzHugh-Nagumo system in RN

Abstract：In this thesis, we study the existences of travelling waves of the diffusive FitzHugh-Nagumo system (DFHN) in RN. This system has a skew-gradient structure as defined by Yanagida as well as a non-local gradient structure. In addition, it also has a monotone system structure on some parameter ranges by a suitable transformation. For bounded domains, the variational approach is applied to construct steady states of (DFHN) with Dirichlet or/and Neumann condition. For infinitely cylindrical domains, we study the travelling wave solutions via all of three structures when the diffusion coefficients in the equations are equal. By using the nonlocal variational energy, we establish the existence of a travelling front solution for (DFHN). Our existence result also obtains a variational characterization for the wave speed. On the other hand, using the skew-gradient structure, we give a mini-max formulation of the travelling wave and its speed. For whole domains, we employ the method of super- and subsolutions to establish the existence of monostable-type traveling wave solutions. Moreover, we construct infinitely many standing periodic solutions in RN based on the reflection method.

Time：16:00, June. 04(Mon.), 2012

Place：Room 430, Astronomy and Mathematics Building, National Taiwan University(臺灣大學天文數學館430室)