Convex Lyapunov functionals for non-convex gradient flows: two examples

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• Daniel Matthes (Munich Technical University, Germany)
• Tuesday 11 March 2014, 16:00-17:00
• Nuffield G18.

If you have a question about this talk, please contact José Cañizo.

Note this talk is scheduled on a Tuesday instead of a Wednesday

Various diffusion equations can be written as a gradient flow, i.e., their solutions are curves of steepest descent (with respect to a suitable metric) in some energy landscape (of a suitable potential). If the potential is strictly convex in the considered metric, then one immediately obtains quantitative estimates on the speed of convergence of solutions towards equilibrium.

In this talk, I will discuss two examples in which the potential is not convex, but still good estimates on the long-time asymptotics can be derived by variational methods. The first example (joint with S.Linisi and G.Savare) is a family of fourth order degenerate parabolic equations, which arise e.g. in models for lubrication. The second example (joint work with J.Zinsl) is a system of two nonlinear diffusion equations modeling the aggregation of bacteria.

This talk is part of the Analysis seminar series.

This talk is included in these lists:

• Analysis seminar
• Nuffield G18
• School of Mathematics events

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