Geodesic
Mechanism for the formation of an inhomogeneous nanorelief and bifurcations in a nonlocal erosion equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 1, pp. 74-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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We continue studies of the nonlocal erosion equation that is used as a mathematical model of the formation of a spatially inhomogeneous relief on semiconductor surfaces. We show that such a relief can form as a result of local bifurcations in the case where the stability of the spatially homogeneous equilibrium state changes. We consider a periodic boundary-value problem and study its codimension-$2$ bifurcations. For solutions describing an inhomogeneous relief, we obtain asymptotic formulas and study their stability. The analysis of the mathematical problem is based on modern methods of the theory of dynamical systems with an infinite-dimensional phase space, in particular, on the method of integral manifolds and on the theory of normal forms.
Keywords: nanorelief formation, stability, integral manifold, normal form.
Mots-clés : nonlocal erosion equation, bifurcation 
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D. A. Kulikov. Mechanism for the formation of an inhomogeneous nanorelief and bifurcations in a nonlocal erosion equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 1, pp. 74-92. http://geodesic.mathdoc.fr/item/TMF_2024_220_1_a5/

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