Seminar on Nonlinear Partial Differential Equations

Abstract

Geometrical and Analytical Questions in Nonlinear Elasticity.- An Introduction to Euler's Equations for an Incompressible Fluid.- Linearizing Flows and a Cohomology Interpretation of Lax Equations.- The Ricci Curvature Equation.- A Walk Through Partial Differential Equations.- Remarks on Zero Viscosity Limit for Nonstationary Navier-Stokes Flows with Boundary.- Free Boundary Problems in Mechanics.- The Method of Partial Regularity as Applied to the Navier-Stokes Equations.- Shock Waves, Increase of Entropy and Loss of Information.- Stress and Riemannian Metrics in Nonlinear Elasticity.- The Cauchy Problem and Propagation of Singularities.- Analytical Theories of Vortex Motion.- The Minimal Surface Equation.- A Survey of Removable Singularities.- Applications of the Maximum Principle.- Minimax Methods and Their Application to Partial Differential Equations.- Analytic Aspects of the Harmonic Map Problem.- Equations of Plasma Physics.