Videos

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.
Supplementary Materials