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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Chen, Gui-Qiang, 1963- (Autor), Feldman, Mikhail, 1960- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, 2018.
Colección:Annals of mathematics studies ; no. 197.
Temas:
Shock waves > Diffraction.
Shock waves > Mathematics.
Von Neumann algebras.
Ondes de choc > Mathématiques.
Algèbres de Von Neumann.
MATHEMATICS > General.
Shock waves > Diffraction
Von Neumann algebras
A priori estimate.
Accuracy and precision.
Algorithm.
Andrew Majda.
Attractor.
Banach space.
Bernhard Riemann.
Big O notation.
Boundary value problem.
Bounded set (topological vector space).
C0.
Calculation.
Cauchy problem.
Coefficient.
Computation.
Computational fluid dynamics.
Conjecture.
Conservation law.
Continuum mechanics.
Convex function.
Degeneracy (mathematics).
Demetrios Christodoulou.
Derivative.
Diffraction.
Dimension.
Directional derivative.
Dirichlet boundary condition.
Dirichlet problem.
Dissipation.
Ellipse.
Elliptic curve.
Elliptic partial differential equation.
Embedding problem.
Equation solving.
Equation.
Estimation.
Euler equations (fluid dynamics).
Existential quantification.
Fixed point (mathematics).
Flow network.
Fluid dynamics.
Fluid mechanics.
Free boundary problem.
Function (mathematics).
Function space.
Fundamental class.
Fundamental solution.
Fundamental theorem.
Hyperbolic partial differential equation.
Initial value problem.
Iteration.
Laplace's equation.
Linear equation.
Linear programming.
Linear space (geometry).
Mach reflection.
Mathematical analysis.
Mathematical optimization.
Mathematical physics.
Mathematical problem.
Mathematical proof.
Mathematical theory.
Mathematician.
Mathematics.
Melting.
Monotonic function.
Neumann boundary condition.
Nonlinear system.
Numerical analysis.
Parameter space.
Parameter.
Partial derivative.
Partial differential equation.
Phase boundary.
Phase transition.
Potential flow.
Pressure gradient.
Quadratic function.
Regularity theorem.
Riemann problem.
Scientific notation.
Self-similarity.
Special case.
Specular reflection.
Stefan problem.
Structural stability.
Subspace topology.
Symmetrization.
Theorem.
Theory.
Truncation error (numerical integration).
Two-dimensional space.
Unification (computer science).
Variable (mathematics).
Velocity potential.
Vortex sheet.
Vorticity.
Wave equation.
Weak convergence (Hilbert space).
Weak solution.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • I. Shock reflection-diffraction, nonlinear conservation laws of mixed type, and von Neumann's conjectures
  • Shock reflection-diffraction, nonlinear partial differential equations of mixed type, and free boundary problems
  • Mathematical formulations and main theorems
  • Main steps and related analysis in the proofs of the main theorems
  • II. Elliptic theory and related analysis for shock reflection-diffraction
  • Relevant results for nonlinear elliptic equations of second order
  • Basic properties of the self-similar potential flow equation
  • III. Proofs of the main theorems for the sonic conjecture and related analysis
  • Uniform states and normal reflection
  • Local theory and von Neumann's conjectures
  • Admissible solutions and features of problem 2.6.1
  • Uniform estimates for admissible solutions
  • Regularity of admissible solutions away from the sonic arc
  • Regularity of admissible solutions near the sonic arc
  • Iteration set and solvability of the iteration problem
  • Iteration map, fixed points, and existence of admissible solutions up to the sonic angle
  • Optimal regularity of solutions near the sonic circle
  • IV. Subsonic regular reflection-diffraction and global existence of solutions up to the detachment angle
  • Regularity of admissible solutions near the sonic arc and the reflection point
  • Existence of global regular reflection-diffraction solutions up to the detachment angle
  • V. Connections and open problems
  • The full Euler equation and the potential flow equation
  • Shock reflection-diffraction and new mathematical challenges.

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