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Upper bounds on the coarsening rates of discrete ill-posed nonlinear diffusions

John B. Greer
Courant Institute of Mathematical Sciences, NYU


I will discuss a recent proof of a weak upper bound on the coarseningrate of the discrete-in-space version of an ill-posed, nonlineardiffusion equation. The continuum version of the equation violatesparabolicity and lacks a complete well-posedness theory. Inparticular, numerical simulations indicate very sensitive dependenceon initial data. Nevertheless, models based on its discrete-in-spaceversion, which I will discuss, are widely used in a number ofapplications, including population dynamics (chemotactic movement ofbacteria), granular flow (formation of shear bands), and computervision (image denoising and segmentation). The bounds haveimplications for all three applications.
This is joint work with Selim Esedoglu (U. of Michigan Mathematics).

Monday, January 22, 2007
11:00AM AP&M 2402