Initialboundary value problems for hyperbolic systems in regions with corners. I
Author:
Stanley Osher
Journal:
Trans. Amer. Math. Soc. 176 (1973), 141164
MSC:
Primary 35L50
MathSciNet review:
0320539
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Abstract: In recent papers Kreiss and others have shown that initialboundary value problems for strictly hyperbolic systems in regions with smooth boundaries are wellposed 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:
http://dx.doi.org/10.1090/S00029947197303205395
PII:
S 00029947(1973)03205395
Keywords:
Hyperbolic equations,
initial boundary conditions,
symmetrizer,
energy estimate,
wellposedness
Article copyright:
© Copyright 1973 American Mathematical Society
