# 60153

## Автор(ов):

1

Параметры публикации

## Тип публикации:

Статья в журнале/сборнике

## Название:

Multivalued solutions of hyperbolic Monge-Ampère equations: solvability, integrability, approximation

10.1070/SM9171

## Наименование источника:

• Sbornik: Mathematics

Т. 211, № 3

• Москва

## Издательство:

• Turpion Limited

2020

## Страницы:

373-421
Аннотация
Solvability in the class of multivalued solutions is investigated for Cauchy problems for hyperbolic Monge-Ampère equations. A characteristic uniformization is constructed on definite solutions of this problem, using which the existence and uniqueness of a maximal solution is established. It is shown that the characteristics in the different families that lie on a maximal solution and converge to a definite boundary point have infinite lengths. In this way a theory of global solvability is developed for the Cauchy problem for hyperbolic Monge-Ampère equations, which is analogous to the corresponding theory for ordinary differential equations. Using the same methods, a stable explicit difference scheme for approximating multivalued solutions can be constructed and a number of problems which are important for applications can be integrated by quadratures.

## Библиографическая ссылка:

Туницкий Д.В. Multivalued solutions of hyperbolic Monge-Ampère equations: solvability, integrability, approximation // Sbornik: Mathematics. 2020. Т. 211, № 3. С. 373-421.

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