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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Additional Information

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