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.

chapter 2|5 pages

Rigidity and Nonlinear Elasticity

ByRobert V. Kohn

chapter 4|11 pages

Unstable Viscoelastic Fluid Flows

ByM. Slemrod

chapter 5|8 pages

Isolas and Perturbed Bifurcation Theory

ByHerbert B. Keller

chapter 7|13 pages

Solutions of the Korteweg-De Vries Equation

ByAmy Cohen

chapter 8|9 pages

A Three-Phase Free Boundary Problem Arising in Alloy Solidification

ByVasilios Alexiades

chapter 9|8 pages

Spatial Decay for the Navier-Stokes Equations

ByAlan Elcrat

chapter 10|20 pages

A Riemannian Metric for Partial Differential Equations

ByConstantin N. Kockinos

chapter 11|11 pages

Shockless Airfoils for Wings, Compressors, and Turbines

ByP. R. Garabedian

chapter 13|20 pages

Three-Dimensional Nonlinear Evolution of Water Waves

ByW. H. Hui

chapter 16|12 pages

Small Amplitude Stable Wavetrains in Reaction-Diffusion Systems

ByG. Bard Ermentrout

chapter 17|26 pages

A Singularity Theory Approach To Steady-State Bifurcation Theory

ByMartin Golubitsky, David Schaeffer

chapter 19|10 pages

Some Results on a Reaction-Diffusion System

ByMin Ming Tang

chapter 20|14 pages

Discretizing the Sine-Gordon Equation: Geometrical and Group Theoretical Aspects

BySophocles J. Orfanidis

chapter 21|12 pages

Advances in the Numerical Computation of Capillary-Gravity Waves

ByJean-Marc Vanden-Broeck

chapter 23|29 pages

Finite-Difference Scheme for Stationary Navier-Stokes Equations with Variable Coefficients

ByJerzyna Slomczynska, Zbigniew Peradzyński

chapter 24|23 pages

Multiphase Similarity Solutions of Integrable Evolution Equations

ByH. Flaschka, A. C. Newell

chapter 25|18 pages

Solutions of an Internal Wave Equation Describing a Stratified Fluid with Finite Depth

ByJunkichi Satsuma, Mark J. Ablowitz

chapter 26|14 pages

Jump Phenomena

ByEdward L. Reiss

chapter 27|15 pages

Darcy’s Law for Flow in Porous Media and the Two-Space Method

ByJoseph B. Keller

chapter 28|36 pages

Decomposition of Variational Problems and Applications in Finite Elasticity

ByJ. F. Bourgat, R. Glowinski, P. LeTallec