Partial Differential Equations Seminar
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Mon, 16/01/2012 17:00 |
Bernd Kirchheim (OxPDE, University of Oxford) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
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Mon, 23/01/2012 17:00 |
Steve Shkoller (University of California, Davis) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time “splash” singularity, wherein the evolving 2-D hypersurface intersects itself at a point. Our approach is based on the Lagrangian description of the free-boundary problem, combined with novel approximation scheme. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems. This is joint work with Daniel Coutand. | |||
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Mon, 30/01/2012 17:00 |
Kewei Zhang (Swansea University) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| In the first part, a variational model for composition of finitely many strongly elliptic homogenous elastic materials in linear elasticity is considered. The notion of`universal coercivity' for the variational integrals is introduced which is independent of particular compositions of materials involved. Examples and counterexamples for universal coercivity are presented. In the second part, some results of recent work with colleagues on image processing and feature extraction will be displayed. | |||
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Mon, 06/02/2012 17:00 |
J. Sivaloganathan (University of Bath) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
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Mon, 13/02/2012 17:00 |
Bryce McLeod (OxPDE, University of Oxford) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
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Mon, 20/02/2012 17:00 |
Barbara Niethammer (OxPDE, University of Oxford) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
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Mon, 27/02/2012 17:00 |
Peter M. Topping (University of Warwick) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| This talk will consist of a pure PDE part, and an applied part. The unifying topic is mean curvature flow (MCF), and particularly mean curvature flow starting at cones. This latter subject originates from the abstract consideration of uniqueness questions for flows in the presence of singularities. Recently, this theory has found applications in several quite different areas, and I will explain the connections with Harnack estimates (which I will explain from scratch) and also with the study of the dynamics of charged fluid droplets. There are essentially no prerequisites. It would help to be familiar with basic submanifold geometry (e.g. second fundamental form) and intuition concerning the heat equation, but I will try to explain everything and give the talk at colloquium level. Joint work with Sebastian Helmensdorfer. | |||
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Mon, 05/03/2012 17:00 |
Lars Diening (University of Munich) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| We consider the stationary flow of Prandtl-Eyring fluids in two dimensions. This model is a good approximation of perfect plasticity. The corresponding potential is only slightly super linear. Thus, many severe problems arise in the existence theory of weak solutions. These problems are overcome by use of a divergence free Lipschitz truncation. As a second application of this technique, we generalize the concept of almost harmonic functions to the Stokes system. | |||
