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Mass concentration phenomena for the long-wave unstable thin-film equation

Connections for Women on Optimal Transport: Geometry and Dynamics August 22, 2013 - August 23, 2013

August 23, 2013 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Marina Chugunova (Claremont Graduate University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

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
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