Abstract:

In this talk we focus on the uniqueness and spatial decay of higher dimensional cylinder waves for the degenerate Fisher equation with heterogeneous convection.  By applying and extending the generalized center manifold theorem, we get the  precise non-exponential spatial decay of cylinder waves with noncritical speeds. Further by applying the detailed asymptotic estimates and spectral expansion we get the higher order expansion of the cylinder waves with non-critical speeds for the p-degree Fisher equation. In this talk we shall also talk about the uniqueness of the cylinder waves with critical and noncritical speeds.  The talk is based on the joint work with Dr. Junfeng He.