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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Author: Stanley Osher
Journal: Trans. Amer. Math. Soc. 176 (1973), 141-164
MSC: Primary 35L50
DOI: https://doi.org/10.1090/S0002-9947-1973-0320539-5
MathSciNet review: 0320539
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Abstract: In recent papers Kreiss and others have shown that initial-boundary value problems for strictly hyperbolic systems in regions with smooth boundaries are well-posed under uniform Lopatinskiĭ conditions. In the present paper the author obtains new conditions which are necessary for existence and sufficient for uniqueness and for certain energy estimates to be valid for such equations in regions with corners. The key tool is the construction of a symmetrizer which satisfies an operator valued differential equation.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0320539-5
Keywords: Hyperbolic equations, initial boundary conditions, symmetrizer, energy estimate, well-posedness
Article copyright: © Copyright 1973 American Mathematical Society