The Pyramidal Traveling Fronts Of A Time Periodic Diffusion Equation With Degenerate Monostable Nonlinearity

The reaction-diffusion equation has been studied extensively because it can describe many diffusion phenomena in nature.The traveling front,as a type of solution of the reaction-diffusion equation,is classified into planar traveling front and nonplanar traveling front accord-ing to whether the level set is a hyperplane.Different from the planar traveling front,nonplanar traveling front not only has more diverse shapes,but also more complex properties.Besides,due to seasonal and other factors,the environment undergoes periodic changes.Therefore,it is of great theoretical value and practical significance to study the nonplanar traveling front of the time-period reaction-diffusion equation.Thus,this article mainly consider the existence of the nonplanar traveling front of degenerate monostable time periodic reaction-diffusion equation in R~nwith n≥3.Firstly,we give some preliminaries knowledge in Chapter 2.Secondly,in Chapter 3,we discuss the existence of traveling fronts of degenerate monostable reaction-diffusion equation with time period in R~3by constructing suitable supersolution and using the super-sub solution method and comparison principle.Thirdly,in Chapter 4,we use similar method to obtain the existence of n-dimensional periodic pyramid traveling fronts,where n≥4.Finally,we summarize the main finding and advantages of the methodology in Chapter 5.