Abstract:

In this talk we shall talk about our recent works on the stability of cylinder front and asymptotic behavior of solution for the degenerate Fisher type equation. By applying spectral analysis we prove the  exponential stability of all waves in some exponentially weighted spaces for the degenerate Fisher type equation. Based on the precise spatial decay of the waves for the p-degree Fisher equation, by applying sub-supper solution method we prove the Lyapunov  stability  of waves with noncritical speeds in some polynomially weighted spaces and global exponential stability of waves with critical speeds. We shall also investigate the asymptotic behavior of solution with more general initial data. The talk is based on the joint work with Dr. Junfeng He.