Persistence and asymptotic behavior of classical solutions to a parabolic-parabolic chemotaxis model with a mixed operator and logistic source on \({\mathbb {R}}^N\)
摘要
In recent years, scientists found that the movement and interaction of some organisms occur not only between adjacent spatial positions, but also between non adjacent spatial positions. The movement and interaction of such organisms cannot be simply described by local diffusion or nonlocal diffusion. Therefore, we consider a parabolic-parabolic chemotaxis model driven by a mixed diffusion operator which is a combination of local diffusion operator and nonlocal diffusion operator. We investigate the global existence and boundedness of classical solution of this mixed diffusion model and the persistence and asymptotic behavior of global classical solution with strictly positive initial data.