A variational approach to parabolic equations and systems via the calculus of variations
Event details
| Date | 19.06.2015 |
| Hour | 15:15 |
| Speaker | Prof. Paolo Marcellini, Université de Florence, Italie |
| Location |
MA A3 31
|
| Category | Conferences - Seminars |
We introduce the notion of "variational solutions", also named "parabolic minimizers", to a class of evolutionary problems possessing a variational structure.
The advantage of these variational solutions stems from the fact that they might exist even in situations where the associated nonlinear parabolic system makes no sense. We should compare with the stationary case, where it is possible to establish the existence of minimizers by the direct methods of the calculus of variations in fairly general situations, whereas additional stronger assumptions are needed to guarantee that the minimizers fulfill the Euler-Lagrange system.
Under reasonable assumptions, such as coercivity and convexity of the energy function, the variational solution exists and is unique. Under further natural growth conditions, the variational solution is also the unique weak solution to the associated Cauchy-Dirichlet problem.
This is a joint collaboration with V.Bögelein and F.Duzaar.
The advantage of these variational solutions stems from the fact that they might exist even in situations where the associated nonlinear parabolic system makes no sense. We should compare with the stationary case, where it is possible to establish the existence of minimizers by the direct methods of the calculus of variations in fairly general situations, whereas additional stronger assumptions are needed to guarantee that the minimizers fulfill the Euler-Lagrange system.
Under reasonable assumptions, such as coercivity and convexity of the energy function, the variational solution exists and is unique. Under further natural growth conditions, the variational solution is also the unique weak solution to the associated Cauchy-Dirichlet problem.
This is a joint collaboration with V.Bögelein and F.Duzaar.
Links
Practical information
- General public
- Free
Organizer
- Prof. Bernard Dacorogna
Contact
- Virginie Ledouble