Existence and stability of global solutions for a cross-diffusion predator–prey model with sex-structure

By means of the energy estimates and the bootstrap arguments, this thesis investigates the global existence of solutions for a cross-diffusion predator–prey model with sex-structure when the space dimension is less than ten. Furthermore, by constructing a Lyapunov function, the sufficient condition of global asymptotic stability of the positive equilibrium point for the model is given.