The conservation law of mass, also called the continuity equation, is a fundamental law in physics. In this talk, first, we derive the velocity in order to guarantee energy dissipation for given free energy with the spatial inhomogeneous absolute temperature along with the conservation law. The spatial inhomogeneous absolute temperature yields nonlinearity, in contrast with the homogeneous case. As a result, the conservation law turns into a non-linear Fokker-Planck model. Next, we study mathematical analysis, especially long-time asymptotics of the model. This analysis is based on so-called entropy dissipation methods for the linear Fokker-Planck equation. If time permits, we will explain the connection to the grain boundary motion.

Note: This seminar will be held as a Zoom online seminar (only NLPDE seminar members may attend in person).