On stiff problems via Dirichlet forms

Abstract

The stiff problem is concerned with a thermal conduction model with a singular barrier of zero volume. A special case related to one-dimensional Brownian motion is studied in [Lejay, Ann. Appl. Probab., 2016], where the so-called snapping out Brownian motion is constructed and served as the probabilistic interpretation of the stiff problem. In this talk, we shall study the general stiff problem in several cases, including one-dimensional diffusions and two-dimensional Brownian motion. It appears that phase transition will appear, depending on the thermal conductance of the singular barrier, and we shall give probabilistic descriptions of the phases arising in the stiff problem. This talk is based on an ongoing work with Liping Li.