Study On The Propagation Phenomena Of A Nonlocal Diffusion Convection Model

It is well know that traveling wave solutions,as a kind of special solution to evolution equation,can reflect the population development,migration and invasion well.This thesis studies the propagation phenomena of a nonlocal diffusion population model with convection as follow.ut(t,x)=(J*u-u)(t,x)+(G*u-u)(t,x)+g(u).Different from the research on nonlocal diffusion equation in the literature,this thesis introduces convective term(G*u-u)(t,x)for the first time,considering the influence of external circumstance to the diffusion of population.Among the term G is an asymmetric kernel function.Through the upper and lower solutions and monotonic iteration method,it proves that the model has a minimum propagation speed c*? Rwhich makes the model to have a monotonous traveling wave solution if c?c*while there is no traveling wave solution if c<c*.Especially,when the propagation speed c?c*as well as c ?0,through some analysis techniques it proves that all traveling wave solutions are strictly monotonic and unique in the sense of translation invariance.The results of this research illustrate that the effect of convection doesn't affect the occurrence of the propagation phenomena,but the direction of propagation.It means the negative propagation speed c may occur under the effect of convection.