Traveling Wave Solutions And Spreading Speeds For Two Types Of Reaction-Diffusion Systems

In recent decades,various discrete diffusion systems and nonlocal dispersal sys-tems have been widely concerned by scholars.This is because they can describe some practical problems in nature more accurately.In the study of these system-s,the asymptotic spreading speeds and traveling wave solutions are the focus of the research.The asymptotic spreading speed can describe the invasion speed of biological population and the propagation speed of epidemic disease,and traveling wave solutions can explain the phenomena of finite speed propagation and oscil-lation in nature.Therefore,in this thesis,we are mainly concerned the traveling wave solutions and asymptotic spreading speeds of two types of reaction-diffusion systems.Firstly,we deals with the global stability of traveling waves of a spatially dis-crete diffusion system with time delay and without quasi-monotonicity.By selecting appropriate weighted functions,using the the weighted energy method and Fourier transform,we prove that the monotone or non-monotone traveling waves are expo-nentially stable in L?(R)x L?(R)with the exponential convergence rate e-?t for some constant ?>0.Secondly,we are devoted to the study of spatial dynamics of a mutualistic sys-tem of mistletoes and birds with nonlocal dispersal.By using the theory of asymp-totic spreading speed and travelling waves for monotone semi-flows,we establish the existence of the asymptotic spreading speeds and traveling wave solutions,and pro-vide the upper and lower bound estimates of the asymptotic spreading speeds of c*.The results show that the asymptotic spreading speed coincides with the minimal speed of traveling wave solutions.