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Title: 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:
 [1]
  1. 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}
}