# Second-order hyperbolic equations with strong characteristic degeneracy at the initial hypersurface

## Abstract

In place of the Cauchy problem, a problem without initial data but with constraints on the admissible growth of the solution as t{yields}0 and as |x|{yields}{infinity} is discussed. The unique solubility in certain Sobolev-type weighted spaces is proved. The smoothness properties of generalized solutions are studied.

- Authors:

- State Academy of Consumer Services, Moscow Region (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21202925

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 191; Journal Issue: 4; Other Information: DOI: 10.1070/SM2000v191n04ABEH000469; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAUCHY PROBLEM; EQUATIONS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; ROUGHNESS

### Citation Formats

```
Deryabina, A V.
```*Second-order hyperbolic equations with strong characteristic degeneracy at the initial hypersurface*. United States: N. p., 2000.
Web. doi:10.1070/SM2000V191N04ABEH000469; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Deryabina, A V.
```*Second-order hyperbolic equations with strong characteristic degeneracy at the initial hypersurface*. United States. doi:10.1070/SM2000V191N04ABEH000469; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Deryabina, A V. Sun .
"Second-order hyperbolic equations with strong characteristic degeneracy at the initial hypersurface". United States. doi:10.1070/SM2000V191N04ABEH000469; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21202925,
```

title = {Second-order hyperbolic equations with strong characteristic degeneracy at the initial hypersurface},

author = {Deryabina, A V},

abstractNote = {In place of the Cauchy problem, a problem without initial data but with constraints on the admissible growth of the solution as t{yields}0 and as |x|{yields}{infinity} is discussed. The unique solubility in certain Sobolev-type weighted spaces is proved. The smoothness properties of generalized solutions are studied.},

doi = {10.1070/SM2000V191N04ABEH000469; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 4,

volume = 191,

place = {United States},

year = {2000},

month = {4}

}

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