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On the Cauchy Problemfor a One-DimensionalLoaded ParabolicEquation of a SpecialForm : научноеиздание Frolenkov I.V.Yarovaya M.A.2021 год

On the Cauchy Problem for a One-Dimensional Loaded Parabolic Equation of a Special Form : научное издание
статья из журнала

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База данных: Каталог библиотеки СФУ
Библиографическое описание: On the Cauchy Problem for a One-Dimensional Loaded Parabolic Equation of a Special Form : научное издание / I. V. Frolenkov, M. A. Yarovaya. - Текст : непосредственный // Journal of Mathematical Sciences. - 2021. - Т. 254, № 6. - P. 761-775. - ISSN 1072-3374. - ISSN 1573-8795, DOI 10.1007/s10958-021-05338-x.
Аннотация: In this paper, we consider a loaded parabolic equation of a special form in an unbounded domain with Cauchy data. The equation is one-dimensional and its right-hand side depends on the unknown function u(t, x) and traces of this function and its derivatives by the spatial variable at a finite number of different points of space. Such equations appear after the reduction of some identification problems for coefficients of one-dimensional parabolic equations with Cauchy data to auxiliary direct problems. We obtain sufficient conditions of the global solvability and sufficient conditions of the solvability of the problem considered in a small time interval. We search for solutions in the class of sufficiently smooth bounded functions. We examine the uniqueness of the classical solution found and prove the corresponding sufficient conditions. We also obtain an a priori estimate of a solution that guarantees the continuous dependence of the solution on the right-hand side of the equation and the initial conditions.
Год издания: 2021
Авторы: Frolenkov I.V. , Yarovaya M.A.
Издательство: Plenum Publishers, New York
Источник: Journal of Mathematical Sciences
Выпуск: Т. 254, № 6
Номера страниц: 761-775
Держатель оригинала документа: Institute of Mathematics and Computer Science,Siberian Federal University
Количество экземпляров:
Твёрдая копия издания отсутствует в фонде библиотеки

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