Boundedness and Asymptotic Stability of Solutions for Fully Parabolic Chemotaxis‐Competition System With Loop and Nonlocal Kinetics

ABSTRACT This article deals with the following fully parabolic chemotaxis‐competition system with loop and nonlocal kinetics subject to homogeneous Neumann boundary conditions in an arbitrary smooth bounded domain , where , , with . Under the appropriate assumption of initial data regularity, it is shown that the corresponding initial‐boundary value problem admits a unique global and uniformly bounded solution under some suitable parameter conditions in any spatial dimension. Furthermore, based on some appropriate functionals, the globally asymptotic stabilization of coexistence and semi‐coexistence steady states is studied.