Controllability under constraints of heat processes
- 报告人： Enrique ZUAZUAProfessor
- 报告人单位： DeustoTech-Bilbao & UAM-Madrid & LJLL-Paris
- 报告地址： 长江数学中心302(2) ,长江数学中心409
- 报告时间： 7月19、20日、21日14:00-17:00,24日 08:00-11:00
The free heat equation is well known to preserve the non-negativity of solutions.On the other hand,due to the infinite velocity of propagation,the heat equation is null-controllable in an arbitrary small time interval.The following question then arises naturally:Can the heat dynamics be controlled under a positivity constraint on the state,requiring that the state remains non-negative all along the controlled time dependent trajectory?
In this series of lectures we will show that,if the control time is large enough,constrained controllability holds.We will also show that it fails to be true if the control time is too short.In other words,despite of the infinite velocity of propagation,under the natural positivity constraint on the state,controllability fails when the time horizon is too short.Links with other related topics such as finite-dimensional systems,sparse control,the turnpike property and the control of viscous Hamilton-Jacobi equations will also be discussed.We shall present a list of open problems and subjects for further investigation.(This presentation is based on joint work with Jérôme Lohéac and Emmanuel Trélat)