Asymptotic Behavior Of Pulsating Fronts And Entire Solutions For Reaction Advection Diffusion Equations In Periodic Media

In the study of ecology, biology, and so on, all biotic populations live in some space region, where the external environment including food, humidity and tem-perature changes with the location and time periodically. The periodic variation of media also happens in the fields of physics, engineering and chemistry. There-fore, it is of great significance to study the reaction-advection-diffusion equations in periodic media. In this paper, we study the asymptotic behavior of pulsating fronts and entire solutions of reaction-advection-diffusion equations in periodic media.Firstly, we mainly discuss the research background and give a brief intro-duction to the problem of this article.Secondly, we study the asymptotic behavior of pulsating fronts of reaction-advection-diffusion equations with bistable nonlinearity in periodic media. By using comparison principle and the method of super-subsolutions, we obtain that the pulsating fronts is exponential decay as sâ†'±∞.Lastly, we study the entire solutions of the above equation. Assume that the equation admits three equilibria:one is linearly unstable and the others are linearly stable and that there are different pulsating fronts connecting any two of them. Utilizing the previous conclusion that pulsating fronts decay exponentially, we get some prior estimates. Then we construct suitable sub-super solutions. After that, we establish two different types of pulsating entire solutions and obtain the qualitative properties of them by combing comparison principle with sub-super solution method.