Nonlinear Partial Differential Equations in Engineering and Applied Science
Volume 54
Lecture Notes in Pure and Applied Mathematics Series

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.

1. On the Existence of Hydrostatic Pressure in Regular Finite Deformations of Incompressible Hyperelastic Solids 2. Rigidity and Nonlinear Elasticity 3. Electrical Interactions Between Parallel Nerve Fibers: A Model and Some Results 4. Unstable Viscoelastic Fluid Flows 5. Isolas and Perturbed Bifurcation Theory 6. On the Structure of the Errors Made in Mixed Finite Element Methods 7. Solutions of the Korteweg-De Vries Equation 8. A Three-Phase Free Boundary Problem Arising in Alloy Solidification 9. Spatial Decay for the Navier-Stokes Equations 10. A Riemannian Metric for Partial Differential Equations 11. Shockless Airfoils for Wings, Compressors, and Turbines 12. Some Singularly Perturbed Nonlinear Boundary Value Problems of Elliptic Type 13. Three-Dimensional Nonlinear Evolution of Water Waves 14. A Comparative Study of Numerical Schemes for the Solution of Two-Dimensional Advection Flows 15. Decay of Solutions to the Korteweg De Vries-Burger Equation and to Parabolic Conservation Laws 16. Small Amplitude Stable Wavetrains in Reaction-Diffusion Systems 17. A Singularity Theory Approach To Steady-State Bifurcation Theory 18. Symmetry Properties and Isolated Singularities of Positive Solutions of Nonlinear Elliptic Equations 19. Some Results on a Reaction-Diffusion System 20. Discretizing the Sine-Gordon Equation: Geometrical and Group Theoretical Aspects 21. Advances in the Numerical Computation of Capillary-Gravity Waves 22. Classical and Quantum Dynamics of Integrable Nonlinear Field Theories 23. Finite-Difference Scheme for Stationary Navier-Stokes Equations with Variable Coefficients 24. Multiphase Similarity Solutions of Integrable Evolution Equations 25. Solutions of an Internal Wave Equation Describing a Stratified Fluid with Finite Depth 26. Jump Phenomena 27. Darcy's Law for Flow in Porous Media and the Two-Space Method 28. Decomposition of Variational Problems and Applications in Finite Elasticity

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Robert L. Sternberg