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Multi-dimensional hyperbolic partial differential equationsFirst-order systems and applications$
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Sylvie Benzoni-Gavage and Denis Serre

Print publication date: 2006

Print ISBN-13: 9780199211234

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199211234.001.0001

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VARIABLE-COEFFICIENTS INITIAL BOUNDARY VALUE PROBLEMS

VARIABLE-COEFFICIENTS INITIAL BOUNDARY VALUE PROBLEMS

Chapter:
(p.220) 9 VARIABLE-COEFFICIENTS INITIAL BOUNDARY VALUE PROBLEMS
Source:
Multi-dimensional hyperbolic partial differential equations
Author(s):

Sylvie Benzoni-Gavage

Denis Serre

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199211234.003.0009

This chapter turns to linear IBVPs with variable coefficients. The techniques mix those of Chapters 2 and 4. Dissipative boundary symmetrizers have now variable coefficients, and are viewed as symbolic symmetrizers, from which the chapter builds functional dissipative symmetrizers. The latter are used to establish a priori estimates. The duality method is then employed for proving well-posedness.

Keywords:   energy estimates, functional dissipative symmetrizers, symbolic boundary symmetrizers, duality method, well-posedness, regularity

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