1st Edition
Nonlinear Partial Differential Equations in Engineering and Applied Science
In this volume are twenty-eight papers from the Conference on Nonlinear Partial Differential Equationsin Engineering and Applied Science, sponsored by the Office of Naval Research and held at the Universityof Rhode Island in June, 1979. Included are contributions from an international group of distinguishedmathematicians, scientists, and engineers coming from a wide variety of disciplines and having a commoninterest in the application of mathematics, particularly nonlinear partial differential equations, to realworld problems.The subject matter ranges from almost purely mathematical topics in numerical analysis and bifurcationtheory to a host of practical applications that involve nonlinear partial differential equations, suchas fluid dynamics, nonlinear waves, elasticity, viscoelasticity, hyperelasticity, solitons, metallurgy, shocklessairfoil design, quantum fields, and Darcy's law on flows in porous media.Non/inear Partial Differential Equations in Engineering and Applied Science focuses on a variety oftopics of specialized, contemporary concern to mathematicians, physical and biological scientists, andengineers who work with phenomena that can be described by nonlinear partial differential equations.
Contributors
Introduction
On the Existence of Hydrostatic Pressure in Regular Finite Deformations of Incompressible Hyperelastic Solids
P. LeTallec and J.T. Oden
Rigidity and Nonlinear Elasticity
Robert V. Kohn
Electrical Interactions Between Parallel Nerve Fibers: A Model and Some Results
Johnathan Bell
Unstable Viscoelastic Fluid Flows
M. Slemrod
Isolas And Perturbed Bifurcation Theory
Herbert B. Keller
On the Structure of the Errors Made in Mixed Finite Element Methods
George J. Fix
Solutions of the Korteweg-Devries Equation
Amy Cohen
A Three-Phase Free Boundary Problem Arising in Alloy Solidification
Vasilios Alexiades
Spatial Decay for the Navier-Stokes Equations
Alan Elcrat
A Riemannian Metric For Partial Differential Equations
Constantin N. Kockinos
Shockless Airfoils for Wings, Compressors, and Turbines
P.R. Garabedian
Some Singularly Perturbed Nonlinear Boundary Value Problems of Elliptic Type
F.A. Howes
Three-Dimensional Nonlinear Evolution of Water Waves
W.H. Hui
A Comparative Study of Numerical Schemes for the Solution of Two-Dimensional Advection Flows
J. N. Reddy and J. D. Warburton
Decay of Solutions to the Korteweg De Vries-Burger Equation and to Parabolic Conservation Laws
Maria Elena Schonbek
Small Amplitude stable Wavetrains in Reaction-Diffusion Systems
G.Bard Ermentrout
A Singularity Theory Approach to Steady-State Bifurcation Theory
Martin Golubitsky and David Schaeffer
Symmetry Properties and Isolated Singularities of Positive Solutions of Nonlinear Elliptic Equations
Basilis Gidas
Some Results on a Reaction-Diffusion System
Min Ming Tang
Discretizing the Sine-Gordon Equation: Geometrical and group Theoretical Aspects
Sophocles J. Orfanidis
Advances in the Numerical Computation of Capillary-Gravity Waves
Jean-Marc Vanden-Broeck
Classical and Quantum Dynamics of Integrable Nonlinear Field Theories
A. Jevicki
Finite-Difference Scheme for Stationary Navier-Stokes Equations with Variable Coefficients
Jerzyna Slomoczynska and Zbigniew Peradzyfsky
Jump Phenomena
Edward L. Reiss
Darcy’s Law For Flow in Porous Media and the Two-Space Method
Joseph B. Keller
Decomposition of Variational Problems and Applications in Finite Elasticity
J. F. Bourgat, R. Glowinski, and P. LeTallec
Biography
Robert L. Sternberg