Hyperbolic Systems with Analytic Coefficients Well-posedness of the Cauchy Problem
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 ord...
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| Format: | eBook |
| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2014
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| Series: | Lecture Notes in Mathematics
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| Genre/form: | elektronické knihy |
| ISBN: | 978-3-319-02273-4 9783319022727 9783319022741 |
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| Online Access: | Plný text |
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| 020 | |a 978-3-319-02273-4 |9 9783319022734 | ||
| 024 | 7 | |a 10.1007/978-3-319-02273-4 |2 doi | |
| 040 | |a DE-He213 |b cze |d ABA013 | ||
| 072 | 7 | |a 517 |x Matematická analýza |2 Konspekt |9 13 | |
| 080 | |a 517.95 |2 MRF | ||
| 100 | 1 | |a Nishitani, Tatsuo |4 aut | |
| 245 | 1 | 0 | |a Hyperbolic Systems with Analytic Coefficients |h [elektronický zdroj] : |b Well-posedness of the Cauchy Problem / |c by Tatsuo Nishitani |
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2014 | |
| 300 | |a 1 online zdroj (VIII, 237 p.) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a počítač |b c |2 rdamedia | ||
| 338 | |a online zdroj |b cr |2 rdacarrier | ||
| 490 | 1 | |a Lecture Notes in Mathematics, |x 0075-8434 ; |v 2097 | |
| 505 | 0 | |a Introduction -- Necessary conditions for strong hyperbolicity -- Two by two systems with two independent variables -- Systems with nondegenerate characteristics -- Index | |
| 520 | |a 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. | ||
| 655 | 7 | |a elektronické knihy |7 fd186907 |2 czenas | |
| 659 | 0 | |a Differential equations, partial | |
| 659 | 0 | |a Mathematical physics | |
| 659 | 1 | 4 | |a Partial Differential Equations. |0 http://scigraph.springernature.com/things/product-market-codes/M12155 |
| 659 | 2 | 4 | |a Mathematical Methods in Physics. |0 http://scigraph.springernature.com/things/product-market-codes/P19013 |
| 650 | 0 | 7 | |a diferenciální rovnice parciální |x ma |7 psh7606 |2 psh |
| 650 | 0 | 7 | |a matematická fyzika |x fy |7 psh13654 |2 psh |
| 710 | 2 | |a SpringerLink (online služba) |7 ntk2018999494 | |
| 776 | 0 | 8 | |i Tištěné vydání: |z 9783319022727 |
| 776 | 0 | 8 | |i Tištěné vydání: |z 9783319022741 |
| 830 | 0 | |a Lecture Notes in Mathematics | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-319-02273-4 |y Plný text |
| 910 | |a ABA013 | ||
| 950 | |a Springer |b Lecture Notes in Mathematics 2017 | ||