國立清華大學 數學系

Abstract： Curve shortening equations have been studied for many years. In this talk we consider the curve shortening equation with external driving force depending on the normal vector. For the curve shortening equation without or with a constant driving force, the existences of traveling waves are already known They are both non-compact (unbounded). In this talk, for the case where the external driving force depends on the normal vector, we characterize the property for the existence and non-existence of traveling waves composed of Jordan curve. Finally, we discuss the application to a free boundary problem.