Nonlinear nonlocal reaction-diffusion problem with local reaction

<p style='text-indent:20px;'>In this paper we analyse the asymptotic behaviour of some nonlocal diffusion problems with local reaction term in general metric measure spaces. We find certain classes nonlinear terms, including logistic type for which solutions are globally defined initial data Lebesgue prove satisfy maximum and comparison principles give sign conditions to ensure global bounds large times. also that these possess extremal ordered equilibria solutions, asymptotically, enter between equilibria. Finally a unique positive stationary solution is asymptotically stable nonnegative data. A detailed analysis performed nonlinearities. As model consider here lack smoothing effect, important focus payed along whole on differences results respect diffusion, like Laplacian operator.</p>