On a prey-predator reaction-diffusion system with Holling type III functional response
The authors consider the system named in the title (characterized by prey-dependent feeding rates of the predator) as initial value problem along with Neumann-type boundary conditions in \(n\) spatial dimensions and, defining mild and strong solutions in a Banach space, prove well-posedness of strong solutions (supposing only positivity of the constants involved in the system, and regularity of the initial data), their continuous dependence on the initial values, as well as positivity and boundedness on finite time intervals. Finally, they specialize to one spatial dimension and use the fast Fourier transform coupled with classical fourth-order Runge-Kutta method in time, to obtain numerical approximations.
scientific article; zbMATH DE number 5796765
scientific article