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...
| Main Authors: | , |
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| Format: | Book |
| Language: | English |
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Princeton University Press
2018
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| _version_ | 1797083688887910400 |
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| author | Chen, G-QG Feldman, M |
| author_facet | Chen, G-QG Feldman, M |
| author_sort | Chen, G-QG |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T01:45:00Z |
| format | Book |
| id | oxford-uuid:981d3cd6-b7e1-416a-b170-0bf435dbe7c5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:45:00Z |
| publishDate | 2018 |
| publisher | Princeton University Press |
| record_format | dspace |
| spelling | oxford-uuid:981d3cd6-b7e1-416a-b170-0bf435dbe7c52022-03-27T00:04:45ZThe mathematics of shock reflection-diffraction and von Neumann's conjecturesBookhttp://purl.org/coar/resource_type/c_2f33uuid:981d3cd6-b7e1-416a-b170-0bf435dbe7c5EnglishSymplectic Elements at OxfordPrinceton University Press2018Chen, G-QGFeldman, MThis 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. |
| spellingShingle | Chen, G-QG Feldman, M The mathematics of shock reflection-diffraction and von Neumann's conjectures |
| title | The mathematics of shock reflection-diffraction and von Neumann's conjectures |
| title_full | The mathematics of shock reflection-diffraction and von Neumann's conjectures |
| title_fullStr | The mathematics of shock reflection-diffraction and von Neumann's conjectures |
| title_full_unstemmed | The mathematics of shock reflection-diffraction and von Neumann's conjectures |
| title_short | The mathematics of shock reflection-diffraction and von Neumann's conjectures |
| title_sort | mathematics of shock reflection diffraction and von neumann s conjectures |
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