Global Boundedness Of The Solution Of A Reaction-diffusion Model With Nonlocal Competing Effects

In this paper,two kinds of reaction-diffusion models with nonlocal competition effect are studied,one of which is the Cauchy problem of nonlocal bistable reaction-diffusion equations where N≤2,μ>0,κ>0,γ>0.In this paper,under appropriate conditions on J,the global boundedness of the solution for this nonlocal problem is obtained by using local energy estimation and thermonuclear decomposition.In addition,by constructing local Lyapunov type functional,asymptotic convergence property of hot kernel,error estimation between nonlocal operator and local operator,the known Allee effect is found.The other is the Cauchy problem of nonlinear nonlocal reaction-diffusion equation where u(x,0)=u0(x),it is proved that for 2-2/N<m≤3,the problem admits a global bounded solution by using estimation and Moser iteration.