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Front-type solutions of fractional Allen-Cahn equation. (English) Zbl 1160.35442
Summary: 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 $1<\gamma <2$. 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.

35K57Reaction-diffusion equations
35K55Nonlinear parabolic equations
35K60Nonlinear initial value problems for linear parabolic equations
35Q35PDEs in connection with fluid mechanics
35B40Asymptotic behavior of solutions of PDE
26A33Fractional derivatives and integrals (real functions)
35S10Initial value problems for pseudodifferential operators
Full Text: DOI
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