Mass concentration phenomena for the long-wave unstable thin-film equation
Presenter
August 23, 2013
Keywords:
- Monge mass transport
- Monge-Ampere equation
- non-linear PDE
- optimal transport
- Ricci curvature
- thin-film equation
- lubrication equation
MSC:
- 32W20
- 82C70
- 34B10
- 37-xx
- 37Fxx
- 37Gxx
- 76D08
- 76Dxx
- 74K35
- 74K15
- 74Kxx
Abstract
We study finite speed of support propagation and finite-time blow-up of non-negative solutions for the long-wave unstable thin-film equation. We consider a large range of exponents (n,m) within the super-critical m>n+2 and critical m+2 regimes. For the initial data with negative energy we prove that the solution that blows up in finite time satisfies mass concentration phenomena near the blow-up time. Joint work with: Mary Pugh, Roman Taranets.