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Refined upper bounds on the coarsening rate of discrete, ill-posed diffusion equations

Selim Esedoglu1 and Dejan Slepčev2

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Recommended by A L Bertozzi

We study coarsening phenomena observed in discrete, ill-posed diffusion equations that arise in a variety of applications, including computer vision, population dynamics and granular flow. Our results provide rigorous upper bounds on the coarsening rate in any dimension. Heuristic arguments and the numerical experiments we perform indicate that the bounds are in agreement with the actual rate of coarsening.


PACS

05.60.-k Transport processes

87.23.Cc Population dynamics and ecological pattern formation

02.30.Jr Partial differential equations

45.70.Mg Granular flow: mixing, segregation and stratification

MSC

76T25 Granular flows (See also 74C99, 74E20)

92D25 Population dynamics (general)

60J70 Applications of diffusion theory (population genetics, absorption problems, etc.) (See also 92Dxx)

65F22 Ill-posedness, regularization

76R50 Diffusion (See also 60J60)

Subjects

Mathematical physics

Environmental and Earth science

Statistical physics and nonlinear systems

Dates

Issue 12 (December 2008)

Received 18 March 2008, in final form 27 August 2008

Published 13 November 2008



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