Physical Mathematics and Nonlinear Partial Differential Equations

James H. Lightbourne

Part I 1. Weak Limits of Solutions to Nonlinear Differential Equations 2. Some Models of Glacial Flows 3. Degenerate Diffusion Problems 4. Asymptotic Stability for Stochastic Hereditary Equations 5. Steepest Descent and Time-Stepping for the Numerical Solution of Conservative Equations 6. Lax—Friedricha and the Viscosity—Capillarity Criterion 7. A Singular Free Boundary Problem Part II 8. Global Existence of Classical Solutions to the Equations of Motion for Materials with Fading Memory 9. A Three—Compartment Reaction System with the Effect of Diffusion and Time Delay 10. On Fluid Flow through a Rigid Porous Medium 11. Global Existence of Solutions to the Cauchy Problem for Coupled Maxwell—Schroedinger Equations in Two Space Dimensions 12. Asymptotic Behavior of Solutions of Inhomogeneous Abstract Cauchy Problems 13. Hopf Bifurcation Analysis in a Class of Scalar Functional Differential Equations 14. Existence of Deflagration Waves: Connection to a Degenerate Critical Point 15. The Fissured Medium Equation 16. Nonlinear Homogenization of Two—Phase Flow Equations 17. Rotating States of an Elastic Conductor 18. Stabilization of Solutions of Nonlinear Evolution Equations 19. The Interaction of Transverse Waves for the Vibrating String 20. Global Models for Cosserat Continua and Some Fibrations of Palais, Cerf, and Smale