Gradient-like property and spectral comparison in some reaction-diffusion systems
Yoshihisa MoritaRyukoku University, Japan 下午 2:30–4:00 鴻經館 107 室We are concerned with the FitzHugh-Nagumo equations and some reactoin-diffusion systems with conservation property in a bounded domain with the Neumann boundary condition.
Those systems share the common features such that the Turing instability takes places and the stationary equations can be reduced to a scalar elliptic equation with a nonlocal term, whose solution is provided by a critical point of an energy functional.
Our aim is to show the gradient-like property of each system and the coincidence of the dimension of the unstable manifold of any equilibrium solution and the Morse index of the corresponding critical point of the energy.