1st Edition

Nonlinear Partial Differential Equations in Engineering and Applied Science

    504 Pages
    by CRC Press

    504 Pages
    by CRC Press

    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