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On the Approximation of Solutions to the Heat Equation in the Lebesgue Class L2 by More Regular Solutions

Описание

Тип публикации: статья из журнала

Год издания: 2022

Идентификатор DOI: 10.1134/S0001434622050121

Ключевые слова: approximation theorem, heat equation

Аннотация: Abstract: A criterion for the approximability of all solutions of the heat equation in a bounded cylindrical domain that belong to the Lebesgue class by more regular (e.g., Sobolev) solutions of the same equation in a bounded cylindrical domain with larger base is obtained. Namely, the complement of the smaller base to the larger oПоказать полностьюne must have no (nonempty connected) compact components. As an important corollary, we prove a theorem on the existence of a doubly orthogonal basis for the corresponding pair of Hilbert spaces. © 2022, Pleiades Publishing, Ltd.

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Издание

Журнал: Mathematical Notes

Выпуск журнала: Vol. 111, Is. 5-6

Номера страниц: 782-794

ISSN журнала: 00014346

Издатель: Pleiades journals

Персоны

  • Shlapunov A.A. (Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, Sirius University of Science and Technology, Sochi, 354340, Russian Federation)

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