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Directions in Partial Differential Equations

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

  • 1st Edition - April 8, 1987
  • Latest edition
  • Editors: Michael G. Crandall, Paul H. Rabinowitz, E. L. Turner
  • Language: English

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… Read more

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Description

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


Preface

Symposium Speakers

Contributors

Singular Minimizers and their Significance in Elasticity

Nonlinear Elliptic Equations Involving the Critical Sobolev Exponent—Survey and Perspectives

The Differentiability of the Free Boundary for the n-Dimensional Porous Media Equation

Oscillations and Concentrations in Solutions to the Equations of Mechanics

The Connection Between the Navier-Stokes Equations, Dynamical Systems, and Turbulence Theory

Blow-Up of Solutions of Nonlinear Evolution Equations

Coherence and Chaos in the Kuramoto-Velarde Equation

Einstein Geometry and Hyperbolic Equations

Recent Progress on First Order Hamilton-Jacobi Equations

The Focusing Singularity of the Nonlinear Schrodinger Equation

A Probabilistic Approach to Finding Estimates for the Heat Kernel Associated with a Hormander Form Operator

Discontinuities and Oscillations

The Structure of Manifolds with Positive Scalar Curvature

Index

Product details

  • Edition: 1
  • Latest edition
  • Published: April 28, 1987
  • Language: English

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