Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems

Content Provider	Semantic Scholar
Author	Guès, Olivier Métivier, Guy Williams, Mark Zumbrun, Kevin
Copyright Year	2005
Abstract	Answering a question left open in [MZ2], we show for general symmetric hyperbolic boundary problems with constant coefficients, including in particular systems with characteristics of variable multiplicity, that the uniform Lopatinski condition implies strong L wellposedness, with no further structural assumptions. The result applies, more generally, to any system that is strongly L well-posed for at least one boundary condition. The proof is completely elementary, avoiding reference to Kreiss symmetrizers or other specific techniques. On the other hand, it is specific to the constant-coefficient case; at least, it does not translate in an obvious way to the variable-coefficient case. The result in the hyperbolic case is derived from a more general principle that can be applied, for example, to parabolic or partially parabolic problems like the Navier-Stokes or viscous MHD equations linearized about a constant state or even a viscous shock. ∗Université de Provence, partially supported by European network HYKE, HPRN-CT2002-00282 †Université de Bordeaux, partially supported by European network HYKE, HPRNCT-2002-00282. ‡University of North Carolina, partially supported by NSF grants DMS-0070684 and DMS-0401252 §Indiana University, partially supported by NSF grants DMS-0070765 and DMS0300487; K.Z. thanks Université de Provence for its hospitality during the month-long visit in which this work was carried out.
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Alternate Webpage(s)	https://www.math.u-bordeaux.fr/~gmetivie/gmwz8.pdf
Alternate Webpage(s)	http://www.unc.edu/math/Faculty/williams/var27i.pdf
Language	English
Access Restriction	Open
Subject Keyword	Coefficient Courant–Friedrichs–Lewy condition ELEMENTARY Estimated IBM Notes NARFL gene Navier–Stokes equations Nephrogenic Systemic Fibrosis Parabolic antenna Shock Well-posed problem funding grant multiplicity
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Resource Type	Article