ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 Kawohl, Bernd, University of Cologne, Germany Image processing and anisotropic diffusion The Perona Malik model for anisotropic diffusion is given by the differential equation u_{t} – div(a(|∇u|^{2})∇u) = 0 in Ω × (0, T) under no flux boundary condition a(|∇u|^{2})\frac{∂u}{∂ν} = 0 on ∂Ω×(0, T) and with initial gray scale u(x, 0) = g(x). Here a(s) is positive and decreases to zero as s → ∞. I report on qualitative behaviour of C^{1} solutions to this type of equation, such as maximum and comparison principles, edge enhancement and so on. Reference: B. Kawohl & N. Kutev, Maximum and comparison principle for one-dimensional anisotropic diffusion. Mathematische Annalen (1998), to appear