The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures : : (AMS-197) / / Mikhail Feldman, Gui-Qiang Chen.
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...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English |
---|---|
VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2018] ©2018 |
Year of Publication: | 2018 |
Language: | English |
Series: | Annals of Mathematics Studies ;
197 |
Online Access: | |
Physical Description: | 1 online resource (832 p.) :; 35 line illus. |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
LEADER | 10425nam a22020655i 4500 | ||
---|---|---|---|
001 | 9781400885435 | ||
003 | DE-B1597 | ||
005 | 20220131112047.0 | ||
006 | m|||||o||d|||||||| | ||
007 | cr || |||||||| | ||
008 | 220131t20182018nju fo d z eng d | ||
019 | |a (OCoLC)1029832221 | ||
019 | |a (OCoLC)1032689263 | ||
020 | |a 9781400885435 | ||
024 | 7 | |a 10.1515/9781400885435 |2 doi | |
035 | |a (DE-B1597)477785 | ||
035 | |a (OCoLC)984651973 | ||
040 | |a DE-B1597 |b eng |c DE-B1597 |e rda | ||
041 | 0 | |a eng | |
044 | |a nju |c US-NJ | ||
050 | 4 | |a QC168.85.S45 | |
072 | 7 | |a MAT007020 |2 bisacsh | |
082 | 0 | 4 | |a 531/.1133 |2 23 |
100 | 1 | |a Chen, Gui-Qiang, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 4 | |a The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures : |b (AMS-197) / |c Mikhail Feldman, Gui-Qiang Chen. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2018] | |
264 | 4 | |c ©2018 | |
300 | |a 1 online resource (832 p.) : |b 35 line illus. | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Annals of Mathematics Studies ; |v 197 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Part I: Shock Reflection-Diffraction, Nonlinear Conservation Laws of Mixed Type, and von Neumann's Conjectures -- |t 1. Shock Reflection-Diffraction, Nonlinear Partial Differential Equations of Mixed Type, and Free Boundary Problems -- |t 2. Mathematical Formulations and Main Theorems -- |t 3. Main Steps and Related Analysis in the Proofs of the Main Theorems -- |t Part II: Elliptic Theory and Related Analysis for Shock Reflection-Diffraction -- |t 4. Relevant Results for Nonlinear Elliptic Equations of Second Order -- |t 5. Basic Properties of the Self-Similar Potential Flow Equation -- |t Part III: Proofs of the Main Theorems for the Sonic Conjecture and Related Analysis -- |t 6. Uniform States and Normal Reflection -- |t 7. Local Theory and von Neumann's Conjectures -- |t 8. Admissible Solutions and Features of Problem 2.6.1 -- |t 9. Uniform Estimates for Admissible Solutions -- |t 10. Regularity of Admissible Solutions away from the Sonic Arc -- |t 11. Regularity of Admissible Solutions near the Sonic Arc -- |t 12. Iteration Set and Solvability of the Iteration Problem -- |t 13. Iteration Map, Fixed Points, and Existence of Admissible Solutions up to the Sonic Angle -- |t 14. Optimal Regularity of Solutions near the Sonic Circle -- |t Part IV: Subsonic Regular Reflection-Diffraction and Global Existence of Solutions up to the Detachment Angle -- |t 15. Admissible Solutions and Uniform Estimates up to the Detachment Angle -- |t 16. Regularity of Admissible Solutions near the Sonic Arc and the Reflection Point -- |t 17. Existence of Global Regular Reflection-Diffraction Solutions up to the Detachment Angle -- |t Part V: Connections and Open Problems -- |t 18. The Full Euler Equations and the Potential Flow Equation -- |t 19. Shock Reflection-Diffraction and New Mathematical Challenges -- |t Bibliography -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Shock waves |x Diffraction. | |
650 | 0 | |a Shock waves |x Mathematics. | |
650 | 0 | |a Von Neumann algebras. | |
650 | 7 | |a MATHEMATICS / Differential Equations / Partial. |2 bisacsh | |
653 | |a A priori estimate. | ||
653 | |a Accuracy and precision. | ||
653 | |a Algorithm. | ||
653 | |a Andrew Majda. | ||
653 | |a Attractor. | ||
653 | |a Banach space. | ||
653 | |a Bernhard Riemann. | ||
653 | |a Big O notation. | ||
653 | |a Boundary value problem. | ||
653 | |a Bounded set (topological vector space). | ||
653 | |a C0. | ||
653 | |a Calculation. | ||
653 | |a Cauchy problem. | ||
653 | |a Coefficient. | ||
653 | |a Computation. | ||
653 | |a Computational fluid dynamics. | ||
653 | |a Conjecture. | ||
653 | |a Conservation law. | ||
653 | |a Continuum mechanics. | ||
653 | |a Convex function. | ||
653 | |a Degeneracy (mathematics). | ||
653 | |a Demetrios Christodoulou. | ||
653 | |a Derivative. | ||
653 | |a Diffraction. | ||
653 | |a Dimension. | ||
653 | |a Directional derivative. | ||
653 | |a Dirichlet boundary condition. | ||
653 | |a Dirichlet problem. | ||
653 | |a Dissipation. | ||
653 | |a Ellipse. | ||
653 | |a Elliptic curve. | ||
653 | |a Elliptic partial differential equation. | ||
653 | |a Embedding problem. | ||
653 | |a Equation solving. | ||
653 | |a Equation. | ||
653 | |a Estimation. | ||
653 | |a Euler equations (fluid dynamics). | ||
653 | |a Existential quantification. | ||
653 | |a Fixed point (mathematics). | ||
653 | |a Flow network. | ||
653 | |a Fluid dynamics. | ||
653 | |a Fluid mechanics. | ||
653 | |a Free boundary problem. | ||
653 | |a Function (mathematics). | ||
653 | |a Function space. | ||
653 | |a Fundamental class. | ||
653 | |a Fundamental solution. | ||
653 | |a Fundamental theorem. | ||
653 | |a Hyperbolic partial differential equation. | ||
653 | |a Initial value problem. | ||
653 | |a Iteration. | ||
653 | |a Laplace's equation. | ||
653 | |a Linear equation. | ||
653 | |a Linear programming. | ||
653 | |a Linear space (geometry). | ||
653 | |a Mach reflection. | ||
653 | |a Mathematical analysis. | ||
653 | |a Mathematical optimization. | ||
653 | |a Mathematical physics. | ||
653 | |a Mathematical problem. | ||
653 | |a Mathematical proof. | ||
653 | |a Mathematical theory. | ||
653 | |a Mathematician. | ||
653 | |a Mathematics. | ||
653 | |a Melting. | ||
653 | |a Monotonic function. | ||
653 | |a Neumann boundary condition. | ||
653 | |a Nonlinear system. | ||
653 | |a Numerical analysis. | ||
653 | |a Parameter space. | ||
653 | |a Parameter. | ||
653 | |a Partial derivative. | ||
653 | |a Partial differential equation. | ||
653 | |a Phase boundary. | ||
653 | |a Phase transition. | ||
653 | |a Potential flow. | ||
653 | |a Pressure gradient. | ||
653 | |a Quadratic function. | ||
653 | |a Regularity theorem. | ||
653 | |a Riemann problem. | ||
653 | |a Scientific notation. | ||
653 | |a Self-similarity. | ||
653 | |a Special case. | ||
653 | |a Specular reflection. | ||
653 | |a Stefan problem. | ||
653 | |a Structural stability. | ||
653 | |a Subspace topology. | ||
653 | |a Symmetrization. | ||
653 | |a Theorem. | ||
653 | |a Theory. | ||
653 | |a Truncation error (numerical integration). | ||
653 | |a Two-dimensional space. | ||
653 | |a Unification (computer science). | ||
653 | |a Variable (mathematics). | ||
653 | |a Velocity potential. | ||
653 | |a Vortex sheet. | ||
653 | |a Vorticity. | ||
653 | |a Wave equation. | ||
653 | |a Weak convergence (Hilbert space). | ||
653 | |a Weak solution. | ||
700 | 1 | |a Feldman, Mikhail, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2018 English |z 9783110604252 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2018 |z 9783110603255 |o ZDB-23-DGG |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2018 English |z 9783110604191 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2018 |z 9783110603194 |o ZDB-23-DMA |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press Complete eBook-Package 2018 |z 9783110606591 |
776 | 0 | |c print |z 9780691160559 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9781400885435?locatt=mode:legacy |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400885435 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400885435/original |
912 | |a 978-3-11-060419-1 EBOOK PACKAGE Mathematics 2018 English |b 2018 | ||
912 | |a 978-3-11-060425-2 EBOOK PACKAGE COMPLETE 2018 English |b 2018 | ||
912 | |a 978-3-11-060659-1 Princeton University Press Complete eBook-Package 2018 |b 2018 | ||
912 | |a EBA_BACKALL | ||
912 | |a EBA_CL_MTPY | ||
912 | |a EBA_EBACKALL | ||
912 | |a EBA_EBKALL | ||
912 | |a EBA_ECL_MTPY | ||
912 | |a EBA_EEBKALL | ||
912 | |a EBA_ESTMALL | ||
912 | |a EBA_PPALL | ||
912 | |a EBA_STMALL | ||
912 | |a GBV-deGruyter-alles | ||
912 | |a PDA12STME | ||
912 | |a PDA13ENGE | ||
912 | |a PDA18STMEE | ||
912 | |a PDA5EBK | ||
912 | |a ZDB-23-DGG |b 2017 | ||
912 | |a ZDB-23-DMA |b 2018 | ||
912 | |a ZDB-23-PMB |c 1940 |d 2020 |