
Coarsening Rate of IllPosed Diffusion Equations
Discrete, illposed diffusion equations arise in a variety of contexts: in models of granular flow where they describe the formation of shear bands in a granular material undergoing antiplane shear, in image processing where they consitute one of the most wellknown models  called the PeronaMalik method  for denoising images, and in population dynamics where they describe the chemotactic motion of certain types of bacteria. We study the coarsening phenomena observed in these models using a technique introduced by R. V. Kohn and F. Otto.
 Esedoglu, S.; Greer, J. Upper bounds on the coarsening rate of discrete, illposed, nonlinear diffusion equations. Communications on Pure and Applied Mathematics. 62:1 (2009), pp. 5781.
 Esedoglu, S.; Slepcev, D. Refined upper bounds on the coarsening rate of discrete, illposed diffusion equations. Nonlinearity. 21:12 (2008), pp. 27592776.
Related older works on discrete, illposed diffusion equations:
 Esedoglu, S. An analysis of the PeronaMalik scheme. Communications on Pure and Applied Mathematics. 54 (2001), pp. 14421487.
 Esedoglu, S. Stability properties of the PeronaMalik scheme. SIAM Journal on Numerical Analysis. 44 (2006), pp. 12971313.
