Persistence and extinction in spatial models with a carrying capacity driven diffusion and harvesting

For the reaction-diffusion equation ∂u(t,x)∂t=DΔ(u(t,x)K(t,x))+r(t,x)u(t,x)g(K(t,x),u(t,x))−E(t,x)u(t,x) with the general type of growth, diffusion stipulated by the carrying capacity K and harvesting, existence, positivity, persistence, extinction and stability of solutions are investigated. In numerical simulations, the results are compared to the model with a regular diffusion.