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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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FRIEDRICHS-SYMMETRIC DISSIPATIVE IBVPs

FRIEDRICHS-SYMMETRIC DISSIPATIVE IBVPs

Chapter:
(p.85) 3 FRIEDRICHS-SYMMETRIC DISSIPATIVE IBVPs
Source:
Multi-dimensional hyperbolic partial differential equations
Author(s):

Sylvie Benzoni-Gavage

Denis Serre

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199211234.003.0003

This chapter provides an elementary introduction to Initial Boundary Value Problems (IBVP). It introduces the notion of dissipative boundary condition, here in a classical sense. Such IBVPs can be treated with the Hille-Yosida Theorem. Maximal estimates are obtained that will be considered in subsequent chapters. Strict dissipativeness is crucial for obtaining boundary estimates.

Keywords:   dissipative, strictly dissipative boundary condition, Hille-Yosida Theorem, boundary estimates

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