DYNAMICAL SPIKE SOLUTIONS IN A NONLOCAL MODEL OF PATTERN FORMATION

Abstract. We analyze an integro-differential initial value problem obtained as a shadow-type limit from a system of reaction-diffusion-ODE equations modeling pattern forma-tion. We show that nonlocal terms in such models induce a destabilization of stationary solutions, which may lead to a blowup of spatially inhomogeneous solutions, either in finite or infinite time