Pulsating Fronts For Equations With Combustion Nonlinearities In Spatially Periodic Media

As we all know,the reaction-diffusion equation is a very important type of partial differential equations,which have a wide range of applications in biology,chemistry,physics and other fields.The traveling wave solution,as a special kind of solutions of reaction-diffusion equations,is of great significance both in theory and in application.Environmental heterogeneity is widespread in nature,so the study of inhomogeneous media models is very meaningful.Compared with the situation of homogeneous medium,the situation of inhomogeneous medium is more complicated and the results are richer,which poses many challenges for mathematicians.This paper studies pulsating fronts of reaction-diffusion equations with combustion nonlinearities in spatially periodic media.Chapter 1 mainly introduces the research background,research status,main research issues and results.Chapter 2mainly studies the asymptotic behavior of pulsating fronts.Chapter 3 mainly investigates the second-order continuous Fréchet differentiability of pulsating fronts with respect to the propagation direction.