Directions in Partial Differential Equations

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 28—30, 1985

Michael G. Crandall, Paul H. Rabinowitz, E. L. Turner

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780121952556
• eBook ISBN:
  9781483269245
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Directions in Partial Differential Equations covers the proceedings of the 1985 Symposium by the same title, conducted by the Mathematics Research Center, held at the University of Wisconsin, Madison. This book is composed of 13 chapters and begins with reviews of the calculus of variations and differential geometry. The subsequent chapters deal with the study of development of singularities, regularity theory, hydrodynamics, mathematical physics, asymptotic behavior, and critical point theory. Other chapters discuss the use of probabilistic methods, the modern theory of Hamilton-Jacobi equations, the interaction between theory and numerical methods for partial differential equations. The remaining chapters explore attempts to understand oscillatory phenomena in solutions of nonlinear equations. This book will be of great value to mathematicians and engineers.

Table of contents

• Front Cover
• Directions in Partial Differential Equations
• Copyright Page
• Table of Contents
• Dedication
• Preface
• Symposium Speakers
• Contributors
• Chapter 1. Singular Minimizers and their Significance in Elasticity
• Chapter 2. Nonlinear Elliptic Equations Involving the Critical Sobolev Exponent—Survey and Perspectives
• Chapter 3. The Differentiability of the Free Boundary for the n-Dimensional Porous Media Equation
• Chapter 4. Oscillations and Concentrations in Solutions to the Equations of Mechanics
• Chapter 5. The Connection Between the Navier-Stokes Equations, Dynamical Systems, and Turbulence Theory
• Chapter 6. Blow-Up of Solutions of Nonlinear Evolution Equations
• Chapter 7. Coherence and Chaos in the Kuramoto-Velarde Equation
• Chapter 8. Einstein Geometry and Hyperbolic Equations
• Chapter 9. Recent Progress on First Order Hamilton-Jacobi Equations
• Chapter 10. The Focusing Singularity of the Nonlinear Schrödinger Equation
• Chapter 11. A Probabilistic Approach to Finding Estimates for the Heat Kernel Associated with a Hörmander Form Operator
• Chapter 12. Discontinuities and Oscillations
• Chapter 13. The Structure of Manifolds with Positive Scalar Curvature
• Index