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Spatially Inhomogeneous Solutions to the Nonlocal Erosion Equation with Two Spatial Variables

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We consider the periodic boundary value problem for the nonlocal erosion equation with two spatial variables and obtain sufficient conditions for the existence and stability of spatially inhomogeneous cycles. We analyze the boundary value problem in the case where the length of the domain is essentially greater than the width and obtain conditions for the existence of sufficiently many spatially inhomogeneous cycles depending on both spatial variables. For narrow domains the problem is reduced to analyzing an auxiliary boundary value problem for the Ginzburg–Landau equation.

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Authors and Affiliations

  1. P. G. Demidov Yaroslavl’ State University, 14, Sovetskaya St, Yaroslavl’, 150003, Russia

    D. A. Kulikov

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  1. D. A. Kulikov
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Correspondence to D. A. Kulikov.

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Translated from Problemy Matematicheskogo Analiza 104, 2020, pp. 39-45.

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Kulikov, D.A. Spatially Inhomogeneous Solutions to the Nonlocal Erosion Equation with Two Spatial Variables. J Math Sci 250, 42–50 (2020). https://doi.org/10.1007/s10958-020-04995-8

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  • DOI: https://doi.org/10.1007/s10958-020-04995-8

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