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Zbl 1160.35442
Nec, Y.; Nepomnyashchy, A.A.; Golovin, A.A.
Front-type solutions of fractional Allen-Cahn equation. (English)
[J] Physica D 237, No. 24, 3237-3251 (2008). ISSN 0167-2789

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.

MSC 2000:: *35K57 Reaction-diffusion equations
35K55 Nonlinear parabolic equations
35K60 (Nonlinear) BVP for (non)linear parabolic equations
35Q35 Other equations arising in fluid mechanics
35B40 Asymptotic behavior of solutions of PDE
26A33 Fractional derivatives and integrals (real functions)
35S10 Initial value problems for pseudodifferential operators

Keywords: anomalous front; fractional Allen-Cahn equation; domain wall dynamics

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Zentralblatt MATH Berlin [Germany]