Finite Dimensional Attractor for a One-Phase Stefan Problem with Kinetics

For a one-phase free-boundary problem with kinetics, which is known to generate a rich dynamics, we study evolution of the infinitesimal volume along the trajectories in the attractor. We demonstrate that for sufficiently large m that is defined solely by the properties of the kinetics function the m-dimensional volume decays exponentially. This property combined with the uniform differentiability of the semigroup leads to the conclusion that the Hausdorff dimension of the attractor is finite.