Spatially Inhomogeneous Solutions to the Nonlocal Erosion Equation with Two Spatial Variables
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 essenti...
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| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-10, Vol.250 (1), p.42-50 |
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| container_title | Journal of mathematical sciences (New York, N.Y.) |
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| creator | Kulikov, D. A. |
| description | 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. |
| doi_str_mv | 10.1007/s10958-020-04995-8 |
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| subjects | Boundary value problems Domains Landau-Ginzburg equations Mathematics Mathematics and Statistics Stability analysis |
| title | Spatially Inhomogeneous Solutions to the Nonlocal Erosion Equation with Two Spatial Variables |
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