The Wave Speed And Stability Of Traveling Wave Solutions For Nonlocal Diffusion Systems

In recent decades,traveling wave solutions of nonlocal dispersal systems have attracted extensive attention.Traveling wave solution is a special type of transla-tional invariant solution,which can reveal many important properties of the system itself in the study of mathematical theory.In practice,traveling wave solutions can explain the finite speed propagation and oscillation phenomena in nature.In the s-tudy of travelling wave solutions,the stability and speed of travelling wave solutions are two important problems.In this thesis,the stability and speed of travelling wave solutions for three types of nonlocal dispersal systems are studied.Firstly,the speed sign of bistable wavefront of time-delayed nonlocal dispersal equation is studied.With the help of the asymptotic propagation speed theory of monotone semi-flow,the interval estimation of bistable wave speed is given.Then a general condition for determining the sign of wave speed is established by using the upper and lower solutions,the comparison principle and the global asymptotic stability results of bistable traveling wave solutions.Finally,the results obtained are applied to the nonlocal dispersal equations with two special kernel functions,and the exact conditions for the sign of bistable wave speed are obtained.Secondly,the global asymptotic stability of the traveling wave solution for the two-component nonlocal dispersal L-V competition system is investigated.The competitive system is transformed into a cooperative system by a special trans-formation.Then in the weighted function space,it is proved that the noncritical traveling wave solutions are exponentially asymptotically stable by the comparison principle together with the squeezing technique.Finally,the minimal wave speed of traveling wave solutions to a three-component nonlocal dispersal L-V competition system is studied.By constructing an appropri-ate upper solution,a general condition for the linear determinacy of minimal wave speed is given.Furthermore,an exact condition that only depends on the system parameters is given to ensure the linear determinacy of minimal wave speed.