Ecuación de reacción-difusión. Existencia, unicidad y comportamiento asintótico

Abstract

In this work, the theory of global attractors for parabolics PDEs is studied. We focus on the reaction-diffusion equations and we see as an example the ChaffeeInfante equation. In the first part, we have encompassed elliptic and parabolic linear equations and nonlinear parabolic equations with its corresponding theory of existence and uniqueness of solution. Furthemore, we show some regularity results of weak and strong solutions. In the second part, we treat the theory of dynamical systems. We define the concept of global attractors and we see how they can describe the asymptotic dynamics of the trajectories of the solutions. In addition, we prove a theorem for the existence of global attractors and we study its structure. Finally, we try to apply the previous results to the reaction-difusion equation.