Coarsening in high order, discrete, ill-posed diffusion equations (Q622304)

This paper is concerned with a discrete version of a nonlinear diffusion equation of even degree. The model problem studied by the authors relies on the fourth order diffusion You-Kaveh model that extends the celebrated Perona-Malik model arising in image processing. The main difficulty of such a problem is that it is ill-posed in the continuous variable. The authors provide upper bounds on the coarsening rate by means of a method due to \textit{R. V. Kohn} and \textit{F. Otto} [Commun. Math. Phys. 229, No.~3, 375--395 (2002; Zbl 1004.82011)] for energy driven systems. Various numerical examples are also presented.