[02581] Well-Posedness and smoothness of geometric flows with nonlinear boundary conditions

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G602

Type : Contributed Talk

Abstract : Geometric flows are geometric evolution equations often depicting physical phenomena. We consider a class of geometric flows of order $2m \in 2\mathbb{N}$ describing evolving $n$-manifolds attached to fixed hypersurfaces with some nonlinear boundary conditions. We modify the theory of Maximal Regularity to accommodate quasilinear parabolic PDEs with such boundary conditions. For initial conditions in $W_p^{2m – \frac{2m}{p}}, p\geq \max\{2m, \frac{n}{2m}\}$) we show well-posedness and instantaneous smoothing of the solution on a maximal interval of existence.