The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures (Annals of Mathematics Studies)

Chen, Gui-Qiang; Feldman, Mikhail

ISBN 10: 0691160546 / ISBN 13: 9780691160542

Editore: Princeton University Press, 2018

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Princeton University Press, 2018. Hard cover, first edition. VG condition with no dust jacket, as issued. A nice clean copy. Codice articolo SKU1082825

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Titolo: The Mathematics of Shock ...

Casa editrice: Princeton University Press

Data di pubblicazione: 2018

Legatura: hardcover

Condizione: Very Good

Edizione: First Edition.

Descrizione articolo

Riassunto:

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.

Informazioni sull?autore:

Gui-Qiang G. Chen is the Statutory Professor in the Analysis of Partial Differential Equations at the Mathematical Institute of the University of Oxford, where he is also professorial fellow at Keble College. Mikhail Feldman is professor of mathematics at the University of Wisconsin–Madison.