Convergent difference schemes for nonlinear parabolic equations and mean curvature motion |
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Authors: | Michael G Crandall Pierre-Louis Lions |
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Institution: | (1) Department of Mathematics, University of California, Santa Barbara, CA 93106, USA, US;(2) Ceremade, Université Paris-Dauphine, Place de Lattre de Tassigny, F-75775 Paris 16, France, FR |
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Abstract: | Summary. Explicit finite difference schemes are given for a collection of parabolic equations which may have all of the following complex
features: degeneracy, quasilinearity, full nonlinearity, and singularities. In particular, the equation of “motion by mean
curvature” is included. The schemes are monotone and consistent, so that convergence is guaranteed by the general theory of
approximation of viscosity solutions of fully nonlinear problems. In addition, an intriguing new type of nonlocal problem
is analyzed which is related to the schemes, and another very different sort of approximation is presented as well.
Received January 10, 1995 |
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Keywords: | Mathematics Subject Classification (1991): 35A40 35K55 65M06 65M12 |
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