Lyapunov function and spectrum comparison for a reaction-diffusion system with mass conservation
謝天長 博士國立中央大學數學系 下午 3:00–5:00 健雄館 208-I 室Abstract:
In this talk, I will present Jimbo and Morita’s work on a two-component system of reaction-diffusion equations with mass conservation in a bounded domain with the Neumann boundary conditions. They prove the global boundedness of the solution in L^\infty-norm and the existence of a Lyapunov function. Moreover, by studying the linearized eigenvalue problem of a non-constant equilibrium solution, they provide a comparison theorem for the spectrum between the linearized operators of the system and an appropriate nonlocal scalar equation. As an application of the comparison result they obtain that any stable equilibrium solution must be monotone if the space dimension is one. Is is also shown that a modified system with a new parameter, which covers the present model, possesses a Lyapunov function.