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Fourier Method for a Mixed Problem with the Hill Operator

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Abstract

Boundary value problems for a second-order ordinary differential equation with a nonsmooth potential are considered. An asymptotic representation for an operator semigroup is established based on a previously derived theorem on the eigenvalue asymptotics for the Hill operator. This semigroup is used to describe weak solutions of a mixed problem for a parabolic equation.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00732 for A.G. Baskakov and project no. 18-31-00205 for D.M. Polyakov.

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Correspondence to A. G. Baskakov or D. M. Polyakov.

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Translated by V. Potapchouck

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Baskakov, A.G., Polyakov, D.M. Fourier Method for a Mixed Problem with the Hill Operator. Diff Equat 56, 679–684 (2020). https://doi.org/10.1134/S0012266120060014

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  • DOI: https://doi.org/10.1134/S0012266120060014

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