Hyperbolic Systems with Analytic Coefficients
Well-posedness of the Cauchy Problem
Nishitani, Tatsuo.
creator
author.
SpringerLink (Online service)
text
gw
2014
monographic
eng
access
VIII, 237 p. online resource.
This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearby.
Introduction -- Necessary conditions for strong hyperbolicity -- Two by two systems with two independent variables -- Systems with nondegenerate characteristics -- Index.
by Tatsuo Nishitani.
Mathematics
Differential equations, partial
Mathematical physics
Mathematics
Partial Differential Equations
Mathematical Methods in Physics
QA370-380
515.353
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