Initial-boundary value problems for hyperbolic systems in regions with corners. II

Author:
Stanley Osher

Journal:
Trans. Amer. Math. Soc. **198** (1974), 155-175

MSC:
Primary 35L50

DOI:
https://doi.org/10.1090/S0002-9947-1974-0352715-0

MathSciNet review:
0352715

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Abstract: In the previous paper in this series we obtained conditions equivalent to the validity of certain energy estimates for a general class of hyperbolic systems in regions with corners. In this paper we examine closely the phenomena which occur near the corners if these conditions are violated. These phenomena include: the development of strong singularities (lack of existence), travelling waves which pass unnoticed through the corner (lack of uniqueness), existence and uniqueness if and only if additional conditions are imposed at the corner, and weak solutions which are not strong solutions. We also systematically analyze the conditions for certain important problems. We discuss the physical and computational significance of these results.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0352715-0

Keywords:
Hyperbolic equations,
initial boundary conditions,
energy estimates,
existence and uniqueness

Article copyright:
© Copyright 1974
American Mathematical Society