Hyperbolic Systems with Analytic Coefficients

Well-posedness of the Cauchy Problem

Nonfiction, Science & Nature, Mathematics, Differential Equations, Science, Physics, Mathematical Physics
Cover of the book Hyperbolic Systems with Analytic Coefficients by Tatsuo Nishitani, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Tatsuo Nishitani ISBN: 9783319022734
Publisher: Springer International Publishing Publication: November 19, 2013
Imprint: Springer Language: English
Author: Tatsuo Nishitani
ISBN: 9783319022734
Publisher: Springer International Publishing
Publication: November 19, 2013
Imprint: Springer
Language: English

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.

 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

 

More books from Springer International Publishing

Cover of the book Egyptian Female Labor Force Participation and the Future of Economic Empowerment by Tatsuo Nishitani
Cover of the book Regional Cooperation in South Asia by Tatsuo Nishitani
Cover of the book Wireless Algorithms, Systems, and Applications by Tatsuo Nishitani
Cover of the book Dynamic Modeling, Empirical Macroeconomics, and Finance by Tatsuo Nishitani
Cover of the book Materials Processing Fundamentals 2018 by Tatsuo Nishitani
Cover of the book International Measurement of Disability by Tatsuo Nishitani
Cover of the book Financial Econometrics and Empirical Market Microstructure by Tatsuo Nishitani
Cover of the book Biology, Productivity and Bioenergy of Timber-Yielding Plants by Tatsuo Nishitani
Cover of the book Kautilya and Non-Western IR Theory by Tatsuo Nishitani
Cover of the book Topics in Modal Analysis & Testing, Volume 10 by Tatsuo Nishitani
Cover of the book Local Cosmopolitanism by Tatsuo Nishitani
Cover of the book Outlaw Motorcycle Gangs as Organized Crime Groups by Tatsuo Nishitani
Cover of the book Imaging Convection and Magnetism in the Sun by Tatsuo Nishitani
Cover of the book Reviews in Plasmonics 2016 by Tatsuo Nishitani
Cover of the book Hans J. Morgenthau and the American Experience by Tatsuo Nishitani
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy