# Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems

## Abstract

In this paper, we study the relation between the well-posedness of the inverse problem of the recovering the source in an abstract differential equation and the basis property of a certain class of function systems in a Hilbert space. As a consequence, based on the results concerning the well-posedness of inverse problems, we obtain the Riesz basis property and—under certain additional conditions—the Bari basis property of such systems.

- Authors:

- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771255

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; DIFFERENTIAL EQUATIONS; FUNCTIONS; HILBERT SPACE; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Kostin, A. B., E-mail: abkostin@yandex.ru.
```*Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3799-8.

```
Kostin, A. B., E-mail: abkostin@yandex.ru.
```*Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems*. United States. doi:10.1007/S10958-018-3799-8.

```
Kostin, A. B., E-mail: abkostin@yandex.ru. Tue .
"Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems". United States. doi:10.1007/S10958-018-3799-8.
```

```
@article{osti_22771255,
```

title = {Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems},

author = {Kostin, A. B., E-mail: abkostin@yandex.ru},

abstractNote = {In this paper, we study the relation between the well-posedness of the inverse problem of the recovering the source in an abstract differential equation and the basis property of a certain class of function systems in a Hilbert space. As a consequence, based on the results concerning the well-posedness of inverse problems, we obtain the Riesz basis property and—under certain additional conditions—the Bari basis property of such systems.},

doi = {10.1007/S10958-018-3799-8},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 6,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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