This dissertation is devoted to the understanding of the dynamics of fronts that exhibit coexistence between stable and unstable state in heterogeneous media. With this purpose, we initiated our investigation with a simple model in a discrete medium that describes a chain of dissipative coupled pendulums. Then, we studied the wet oxidation of bidimensional thin aluminum-rich layers into AlOx where the oxidation front has a favored direction of propagation. The dissipative Frenkel-Kontorova model describes a chain of coupled pendulums with dissipation and its solution is called a pi-kink. We report that unlike point-like particles, pi-kinks spread in a pulsating manner. Namely, different parts of the front propagate with the same mean speed, oscillating with the same frequency but different amplitude. The asymptotic behavior of the front allows us to determine, analytically, the minimum average speed as a function of the coupling constant. Due to the discrete nature of the system under study, the determination of the velocity becomes a difficult task. Then, we consider an effective continuous equation with spatial periodic forcing that accounts for the dynamics of the discrete system. Numerical simulations show quite fair agreement between the Frenkel-Kontorova model and the proposed continuous description. We report experimental and theoretical results on the lateral wet oxidation of bidimensional thin aluminum-rich layers into AlOx. To describe the anisotropic propagation of the oxidation front, we introduce a reaction-diffusion model based on the anisotropic catalytic chemical reactions of wet oxidation of AlxGa(1-x)As. Numerical simulations performed with simple and complex geometries are in excellent agreement with the experimental observations. Our method is general and can apply to other oxidation processes.PFCHA-BecasPFCHA-Becas