Construction of a Generalized Solution of a Mixed Problem for the Telegraph Equation: Sequential and Axiomatic Approaches

Автор: Lomov I.S.
Журнал: Differential Equations
Том: 58
Номер: 11
Год издания: 2022
Издательство: Pleiades Publishing, Inc.
Местоположение издательства: New York, USA
Первая страница: 1468
Последняя страница: 1481
DOI: 10.1134/S0012266122110040
Аннотация: Under minimal conditions on the initial data of the mixed problem for the telegraph equation, a generalized solution is obtained in two different ways in the form of a rapidly converging function series—an analog of the well-known d’Alembert formula. The first approach is based on the sequential method: a generalized solution of the problem is determined as the limit of classical solutions of a sequence of problems. The second approach is based on the axiomatic method. Classical solutions are not involved in constructing a generalized solution. Euler’s theory of divergent series with an augmented system of axioms is used. The specific feature of the problem under consideration is the presence of a nonlocal boundary condition in which the value of the function at an interior point of the interval occurs. Both approaches to constructing a generalized solution lead to the same rapidly (exponentially) converging function series.
Добавил в систему: Ломов Игорь Сергеевич

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