Curved Fronts In Reaction-diffusion Equations With Degenerate And Ignition Time-periodic Nonlinearity

There are a lot of diffusion phenomena in biology,physics,chemistry and other fields,most of these phenomena can be described by nonlinear parabolic partial differential equations.This equation has many types of solutions,among these solutions,the theory of planar traveling wave solution is relatively perfect,and many scholars have made contributions in this field.However,due to the fact that the wave shape are affected by the spatial dimension and curvature,it is difficult to describe all the diffusion phenomena only by planar traveling waves,so it is very meaningful to study the nonplanar traveling fronts.In this paper,on the basis of the degenerate and ignition nonlinearity,we further consider curved fronts in reaction-diffusion equations with degenerate and ignition timeperiodic nonlinearity.We first obtain the existence of solutions by using the super-sub solution method,and then establish the stability of the above-mentioned solutions.