Osaka Journal of Mathematics

The hyperbolic region for hyperbolic boundary value problems

Jean-François Coulombel

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Abstract

The well-posedness of hyperbolic initial boundary value problems is linked to the occurrence of zeros of the so-called Lopatinskiĭ determinant. For an important class of problems, the Lopatinskiĭ determinant vanishes in the hyperbolic region of the frequency domain and nowhere else. In this paper, we give a criterion that ensures that the hyperbolic region coincides with the projection of the forward cone. We give some examples of strictly hyperbolic operators that show that our criterion is sharp.

Article information

Source
Osaka J. Math., Volume 48, Number 2 (2011), 457-469.

Dates
First available in Project Euclid: 6 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1315318348

Mathematical Reviews number (MathSciNet)
MR2831981

Zentralblatt MATH identifier
1237.35106

Subjects
Primary: 35L50: Initial-boundary value problems for first-order hyperbolic systems 35L35: Initial-boundary value problems for higher-order hyperbolic equations

Citation

Coulombel, Jean-François. The hyperbolic region for hyperbolic boundary value problems. Osaka J. Math. 48 (2011), no. 2, 457--469. https://projecteuclid.org/euclid.ojm/1315318348


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