Global existence and uniform boundedness in advective Lotka-Volterra competition system with nonlinear diffusion [article]

Qi Wang, Jingyue Yang, Feng Yu
2016 arXiv   pre-print
This paper investigates reaction-advection-diffusion systems with Lotka-Volterra dynamics subject to homogeneous Neumann boundary conditions. Under conditions on growth rates of the density-dependent diffusion and sensitivity functions, we prove the global existence of classical solutions to the system and show that they are uniformly bounded in time. We also obtain the global existence and uniform boundedness for the corresponding parabolic-elliptic systems. Our results suggest that attraction
more » ... (positive taxis) inhibits blowups in Lotka-Volterra competition systems.
arXiv:1605.05308v1 fatcat:d5wykxwgxfeivnaxpw6od7hul4