caa a22 4500 605521883 CHVBK 20210128100742.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10958-015-2284-x doi (NATIONALLICENCE)springer-10.1007/s10958-015-2284-x Kulikov D. Demidov Yaroslavl' State University, Yaroslavl', Russia aut Spatially Inhomogeneous Dissipative Structures in a Periodic Boundary-value Problem for a Nonlocal Erosion Equation [Elektronische Daten] [D. Kulikov] We consider a nonlinear partial differential equation with deviating (transformed) space variable. This equation serves as a mathematical model of formation of the surface patterns on a plate as a result of ionic bombardment. We study a periodic boundary-value problem and propose a mechanism of formation of ripple nanopatterns due to the loss of stability of the flat surface topography. The ripple topography is found as the solution of bifurcation problems studied by using the theory of normal forms and the method of invariant manifolds. For the solutions that describe ripple nanopatterns, we give asymptotic formulas. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 205/6(2015-03-01), 791-805 1072-3374 205:6<791 2015 205 10958 https://doi.org/10.1007/s10958-015-2284-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2284-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kulikov D. Demidov Yaroslavl' State University, Yaroslavl', Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 205/6(2015-03-01), 791-805 1072-3374 205:6<791 2015 205 10958