TY - BOOK
AU - Nishitani, Tatsuo.
ED - SpringerLink (Online service)
TI - Hyperbolic Systems with Analytic Coefficients: Well-posedness of the Cauchy Problem
T2 - Lecture Notes in Mathematics,
SN - 9783319022
AV - QA370-380
U1 - 515.353 23
PY - 2014///
CY - Cham
PB - Springer International Publishing, Imprint: Springer
KW - Mathematics
KW - Differential equations, partial
KW - Mathematical physics
KW - Partial Differential Equations
KW - Mathematical Methods in Physics
N1 - Introduction -- Necessary conditions for strong hyperbolicity -- Two by two systems with two independent variables -- Systems with nondegenerate characteristics -- Index
N2 - 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.
UR - http://dx.doi.org/10.1007/978-3-319-02273-4
ER -