TY  - GEN
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.
DO  - 10.1007/978-3-319-02273-4
DO  - doi
AB  - 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.
T1  - Hyperbolic systems with analytic coefficientswell-posedness of the Cauchy problem /
AU  - Nishitani, Tatsuo,
VL  - 2097
CN  - SpringerLink
CN  - QA377
ID  - 696463
KW  - Cauchy problem.
KW  - Differential equations, Hyperbolic.
SN  - 9783319022734 
SN  - 3319022733 
TI  - Hyperbolic systems with analytic coefficientswell-posedness of the Cauchy problem /
LK  - https://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-02273-4
UR  - https://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-02273-4
ER  -