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The Role of Symmetry and Separation in Surface Evolution and Curve Shortening

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dc.contributor.author Broadbridge, P.
dc.contributor.author Vassiliou, P.
dc.date.accessioned 2019-02-13T18:06:47Z
dc.date.available 2019-02-13T18:06:47Z
dc.date.issued 2011
dc.identifier.citation The Role of Symmetry and Separation in Surface Evolution and Curve Shortening / P. Broadbridge, P. Vassiliou // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 35A30; 35K55; 58J70; 74E10
dc.identifier.other DOI:10.3842/SIGMA.2011.052
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147169
dc.description.abstract With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated solutions is the exact curve shortening flow of a closed, convex ''oval''-shaped curve and another is the smoothing of an initial periodic curve that is close to a square wave. The types of anisotropic evaporation coefficient are found for which the evaporation-condensation evolution does or does not have solutions that are analogous to the basic solutions of the CSE, namely the grim reaper travelling wave, the homothetic shrinking closed curve and the homothetically expanding grain boundary groove. Using equivalence classes of anisotropic diffusion equations, it is shown that physical models of evaporation-condensation must have a diffusivity function that decreases as the inverse square of large slope. Some exact separated solutions are constructed for physically consistent anisotropic diffusion equations. uk_UA
dc.description.sponsorship This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and SpecialFunctions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html. This paper is submitted in appreciation of the valuable on-going contributions of Professor Willard Miller Jr. The first author gratefully acknowledges support by the Australian Research Council under project DP1095044. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title The Role of Symmetry and Separation in Surface Evolution and Curve Shortening uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA

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