Geodesic
Nonlocal model for the formation of ripple topography induced by ion bombardment. Nonhomogeneous nanostructures
Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 33-50

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А mathematical model for the formation of a non-homogeneous thopography on the surface under ionic bombardment is considered. The principal part of this model is any nonlinear functional-differential equation. The possibility of ripple topography formation is demonstrated by means of the bifurcation theory. Asymptotic formulas for the nanostructures are obtained. In particular, it was shown that the set of these solutions forms the local attractor. But all solutions belonging to this attractor are unstable in the sense of Lyapunov definition.
Keywords: nonlocal model of erosion, ionic bombardment, boundary value problems, stability, attractor.
Mots-clés : bifurcations 
@article{MM_2016_28_3_a2,
     author = {A. N. Kulikov and D. A. Kulikov},
     title = {Nonlocal model for the formation of ripple topography induced by ion bombardment. {Nonhomogeneous} nanostructures},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--50},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_3_a2/}
}
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A. N. Kulikov; D. A. Kulikov. Nonlocal model for the formation of ripple topography induced by ion bombardment. Nonhomogeneous nanostructures. Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 33-50. http://geodesic.mathdoc.fr/item/MM_2016_28_3_a2/