Hyperbolic Systems with Analytic Coefficients: Well-posedness of the Cauchy Problem: 2097 (Lecture Notes in Mathematics) - Tapa blanda

Nishitani, Tatsuo

 
9783319022727: Hyperbolic Systems with Analytic Coefficients: Well-posedness of the Cauchy Problem: 2097 (Lecture Notes in Mathematics)
Tapa blanda
ISBN 10: 3319022725 ISBN 13: 9783319022727
Editorial: Springer, 2013

Sinopsis

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 contain 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.

"Sinopsis" puede pertenecer a otra edición de este libro.

De la contraportada

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2013
Idioma
Inglés
ISBN 10 
3319022725
ISBN 13 
9783319022727
Encuadernación
Tapa blanda
Número de páginas
248
Contacto del fabricante
no disponible
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