Upper bounds on the coarsening rate of discrete, ill-posed nonlinear diffusion equations
dc.contributor.author | Esedoglu, Selim | en_US |
dc.contributor.author | Greer, John B. | en_US |
dc.date.accessioned | 2008-11-03T18:53:43Z | |
dc.date.available | 2010-03-01T21:10:28Z | en_US |
dc.date.issued | 2009-01 | en_US |
dc.identifier.citation | Esedoglu, Selim; Greer, John B. (2009). "Upper bounds on the coarsening rate of discrete, ill-posed nonlinear diffusion equations." Communications on Pure and Applied Mathematics 62(1): 57-81. <http://hdl.handle.net/2027.42/61227> | en_US |
dc.identifier.issn | 0010-3640 | en_US |
dc.identifier.issn | 1097-0312 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/61227 | |
dc.description.abstract | We prove a weak upper bound on the coarsening rate of the discrete-in-space version of an ill-posed, nonlinear diffusion equation. The continuum version of the equation violates parabolicity and lacks a complete well-posedness theory. In particular, numerical simulations indicate very sensitive dependence on initial data. Nevertheless, models based on its discrete-in-space version, which we study, are widely used in a number of applications, including population dynamics (chemotactic movement of bacteria), granular flow (formation of shear bands), and computer vision (image denoising and segmentation). Our bounds have implications for all three applications. © 2008 Wiley Periodicals, Inc. | en_US |
dc.format.extent | 1263634 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.publisher | Wiley Subscription Services, Inc., A Wiley Company | en_US |
dc.subject.other | Mathematics and Statistics | en_US |
dc.title | Upper bounds on the coarsening rate of discrete, ill-posed nonlinear diffusion equations | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | University of Michigan, Department of Mathematics, 3835 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043 | en_US |
dc.contributor.affiliationother | Courant Institute ; National Geospatial Intelligence Agency, 4600 Sangamore Road, Bethesda, MD 20816-5003 | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/61227/1/20259_ftp.pdf | |
dc.identifier.doi | http://dx.doi.org/10.1002/cpa.20259 | en_US |
dc.identifier.source | Communications on Pure and Applied Mathematics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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