PDE Seminar The variational problem for a certain action functional defined on closed curves

2009-04-23 17:00 - 2009-04-23 18:30
Faculty of Science Building 3, 2nd floor, Room 202
Shinya Okabe (Iwate University)
We consider a variational problem for a certain time space functional defined on planar closed curves.The functional is appeared in the action minimization problem for stochastic Allen-Cahn equation.The variational problem is stated as follows: "Let $\Gamma_0$ and $\Gamma_1$ be given planar closedcurves and $T$ be a given positive constant. Then minimize the time space functional over familiesof planar closed curves, which change from $\Gamma_0$ to $\Gamma_1$ in time $T$."In this talk, we focus on an existence of non-radial symmetry critical point of the variational problem,in particular a solvability of an initial final value problem.