Traveling Wave Solutions And Wave Speeds For Two Types Of Nonlocal Diffusion Systems

Since nonlocal diffusion systems have important applications in many disciplines,they have received widespread attention from scholars.In the study of nonlocal diffusion systems,traveling wave solutions is a focus of the research.This is because traveling wave solutions can explain the finite speed propagation and oscillation phenomenon in natural.In this thesis,the existence,stability and speed of traveling wave solutions for two types of nonlocal diffusion systems are studied.In chapter 2,we investigate the existence and stability of traveling wavefronts for a three species L-V competitive-cooperative system with nonlocal diffusion.Firstly,we prove the existence of traveling wavefronts by constructing a pair of suitable upper and lower solutions,applying monotone iteration technique and a limiting argument.Then,we prove the nonexistence of traveling wavefronts by contradiction.Finally,by applying the weighted energy method together with the comparison principle,we prove that the traveling wavefronts with relatively large speeds are exponentially stable as perturbation in some weighted spaces.In chapter 3,we investigate the speed selection for a two species L-V competitive system with local vs.nonlocal diffusions.By a special transformation,we transform the competitive system into cooperative system.Then we employ the upper and lower solutions method to study the minimal wave speed selection:linear or nonlinear.For the linear selection,we concentrate on constructing suitable upper solutions.For the nonlinear selection,we focus on constructing lower solutions.