Palestras e Seminários
06/04/2022
14:00
Online / à distância
Palestrante: Antoine Laurain (IME-USP)
Webinar on Evolution Equations and Dynamical Systems
Resumo: We develop a framework and numerical method for controlling the
full space-time tube of a geometrically driven flow. We consider an optimal
control problem for the mean curvature flow of a curve or surface with a
volume constraint, where the control parameter acts as a forcing term in
the motion law. The control of the trajectory of the flow is achieved by
minimizing an appropriate tracking-type cost functional. The gradient of
the cost functional is obtained via a formal sensitivity analysis of the
space-time tube generated by the mean curvature flow. We show that the
perturbation of the tube may be described by a transverse field satisfying
a parabolic equation on the tube. We propose a numerical algorithm to
approximate the optimal control and show several results in two and three
dimensions demonstrating the efficiency of the approach.
A partir deste semestre, as reuniões serão feitas pelo *Zoom.*
O calendário com palestrantes do próximo semestre se encontra em:
https://sites.google.com/usp.br/evol-eq-and-dyn-systems
