Control of Moving Domains, Shape Stabilization and Variational Tube Formulations
Jean-Paul Zolésio · International series of numerical mathematics · 2007
This paper deals with the control of a moving dynamical domain in which a non cylindrical dynamical boundary value problem is considered. We consider weak Eulerian evolution of domains through the convection of a measurable set by (non necessarily smooth) vector field V . We introduce the concept of tubes by “product space” and we show a closure result leading to existence results for a variational shape principle. We illustrate this by new results: heat equation and wave equation in moving domains with various boundary conditions and also the geodesic characterisation for two Eulerian shape metrics leading to the Euler equation through the transverse field considerations. We consider the non linear Hamilton-Jacobi like equation associated with level set parametrization of the moving domain and give new existence result of possible topological change in finite time in the solution. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.