MARC details
| 000 -LEADER |
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| fixed length control field |
04155cam a22002778i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
137677 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20170517123644.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
160520s2016 riu b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470428570 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510MS |
| Edition number |
23 |
| Item number |
Am512 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Speck, Jared, |
| Relator term |
author |
| 245 10 - TITLE STATEMENT |
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| Title |
Shock formation in small-data solutions to 3D quasilinear wave equations / |
| Statement of responsibility, etc |
Jared Speck. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Providence : |
| Name of publisher, distributor, etc |
American Mathematical Society, |
| Date of publication, distribution, etc |
©2016. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xxiii, 515 pages ; |
| Dimensions |
26 cm. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Mathematical surveys and monographs ; |
| Volume number/sequential designation |
v 214 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. Introduction --<br/>2. Overview of the two main theorems --<br/>3. Initial data, basic geometric constructions, and the future null condition failure factor --<br/>4. Transport equations for the Eikonal function quanities --<br/>5. Connection coefficients of the rescaled frmes and geometric --<br/>6. Construction of the rotation vectorfields and their basic properties --<br/>7. Definition of the commutation vectorfields and deformation tensor calculations --<br/>8. Geometric operator commutator formulas and schematic notation for repeated differentiation --<br/>9. The structure of the wave equation inhomogeneous terms after one commutation --<br/>10. Energy and cone flux definitions and the fundamental divergence identities --<br/>11. Avoiding derivative loss and other difficulties via modified quantities --<br/>12. Small data, sup-norm bootstrap assumptions, and first pointwise estimates --<br/>13. Sharp estimates for the inverse foliation density --<br/>14. Square integral coerciveness and the fundamental square-integral-controlling quantities --<br/>15. Top-order pointwise commutator estimates involving the Eikonal function --<br/>16. Pointwise estimates for the easy error integrands and identification of the difficult error integrands corresponding to the commuted wave equation --<br/>17. Pointwise estimates for the difficult error integrands corresponding to the commuted wave equation --<br/>18. Elliptic estimates and sobolev embedding on the spheres --<br/>19. Square integral estimates for the Eikonal function quantities that do not rely on modified quantities --<br/>20. A priori estimates for the fundamental square-integral-controlling quantities --<br/>21. Local well-posedness and continuation criteria --<br/>22. The sharp classical lifespan theorem --<br/>23. Proof of shock formation for nearly spherically symmetric data --<br/>Appendices. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he provides a sharp description of the blow-up. These results yield a sharp converse of the fundamental result of Christodoulou and Klainerman, who showed that small-datasolutions are global when the null condition is satisfied. Readers who master the material will have acquired tools on the cutting edge of PDEs, fluid mechanics,hyperbolic conservation laws, wave equations, and geometric analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Wave equation |
| General subdivision |
Numerical solutions. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Shock waves |
| General subdivision |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Nonlinear differential equations |
| General subdivision |
Numerical solutions. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Quasilinearization. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
