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The mathematics of shock reflection-diffraction and von Neumann's conjectures /
This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differenti...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2018.
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| Colección: | Annals of mathematics studies ;
no. 197. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws--PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs--mixed type, free boundaries, and corner singularities--that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities. |
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| Descripción Física: | 1 online resource (xiv, 814 pages) |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9781400885435 1400885434 9780691160542 0691160546 9780691160559 0691160554 |