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

For the reaction–diffusion equation ∂ u ( t , x ) ∂ t = D Δ ( 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.