Geodesic
On local bifurcations of spatially inhomogeneous solutions for one functional-differential equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Tome 186 (2020), pp. 67-73

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In this work, we study a nonlocal erosion equation, which simulates the process of nanorelief formation. For a periodic boundary-value problem for the partial functional differential equation, we examine local bifurcations in the cases where homogeneous equilibrium states change their stability. We prove that in the problem considered, subcritical bifurcations occur.
Keywords: functional differential equation, boundary-value problem, stability.
Mots-clés : local bifurcation 
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     author = {D. A. Kulikov},
     title = {On local bifurcations of spatially inhomogeneous solutions for one functional-differential equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {67--73},
     publisher = {mathdoc},
     volume = {186},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_186_a8/}
}
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D. A. Kulikov. On local bifurcations of spatially inhomogeneous solutions for one functional-differential equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Tome 186 (2020), pp. 67-73. http://geodesic.mathdoc.fr/item/INTO_2020_186_a8/