Abstract
Periodic boundary-value problems for two versions of the nonlocal erosion equation are considered. This equation belongs to the class of partial differential equations with deviating spatial arguments. The problem on bifurcations of spatially inhomogeneous solutions to the periodic boundary-value problem is examined. We use the method of invariant manifolds in combination with the theory of normal forms.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 148, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory” (Ryazan, September 15–18, 2016), 2018.
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Kovaleva, A.M., Kulikov, D.A. Bifurcations of Spatially Inhomogeneous Solutions in two Versions of the Nonlocal Erosion Equation. J Math Sci 248, 438–447 (2020). https://doi.org/10.1007/s10958-020-04884-0
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DOI: https://doi.org/10.1007/s10958-020-04884-0
Keywords and phrases
- partial differential equations
- deviating spatial argument
- periodic boundary-value problem
- stability
- bifurcations
- asymptotic formulas