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 Post-Prostatectomy Incontinence by Tatsuo Nishitani
Cover of the book Enterprise Systems. Strategic, Organizational, and Technological Dimensions by Tatsuo Nishitani
Cover of the book Hybrid Machining Processes by Tatsuo Nishitani
Cover of the book Distributed and Sequential Algorithms for Bioinformatics by Tatsuo Nishitani
Cover of the book Small Molecule Therapeutics for Schizophrenia by Tatsuo Nishitani
Cover of the book Cloud Computing by Tatsuo Nishitani
Cover of the book Chemistry of 1,2,3-triazoles by Tatsuo Nishitani
Cover of the book Family Therapy in Global Humanitarian Contexts by Tatsuo Nishitani
Cover of the book Family-Oriented Informed Consent by Tatsuo Nishitani
Cover of the book Supersymmetric Grand Unified Theories by Tatsuo Nishitani
Cover of the book Measurement-Based Care in Mental Disorders by Tatsuo Nishitani
Cover of the book Research and Development in the Academy, Creative Industries and Applications by Tatsuo Nishitani
Cover of the book Advances in Practical Applications of Survivable Agents and Multi-Agent Systems: The PAAMS Collection by Tatsuo Nishitani
Cover of the book Model Validation and Uncertainty Quantification, Volume 3 by Tatsuo Nishitani
Cover of the book Computer Vision – ACCV 2018 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