The Existence Of Global Attractors For The Two Classes Of Reaction-diffusion Equations

In this dissertation, we are concerned with the existence of global attractors for two classes of reaction-diffusion model:a three component reversible autocatalytic reaction-diffusion system with functional response and a partly dissipative reaction-diffusion forest dynamical system. For the first equation, we start by proving the global existence of solution. After that by the asymptotical compactness and the absorbing property of the semi-flow we prove the existence of global attractors. For the second equation, we first obtain the uniform prior estimates with large time of the solutions, and then we prove the asymptotical compactness of the solution semi-flow by cut-off function techniques. Finally we get the existence of global attractor on unbounded domain for this system.We introduce another component to the considered system and are concerned with the influence of external factors, thus the system we study here is clearly more general than the existing ones, and hence our obtained results extend somewhat the existing ones in some references.