Front-type solutions of fractional Allen-Cahn equation |
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| Authors: | Y Nec AA Nepomnyashchy |
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| Institution: | a Department of Mathematics, Technion - Israel Institute of Technology, Haifa, 32000, Israel
b Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston, IL, USA |
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| Abstract: | Super-diffusive front dynamics have been analysed via a fractional analogue of the Allen-Cahn equation. One-dimensional kink shape and such characteristics as slope at origin and domain wall dynamics have been computed numerically and satisfactorily approximated by variational techniques for a set of anomaly exponents 1<γ<2. The dynamics of a two-dimensional curved front has been considered. Also, the time dependence of coarsening rates during the various evolution stages was analysed in one and two spatial dimensions. |
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| Keywords: | 64 60 -i |
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