As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs).This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.

On the Global in Time Solvability of the Cauchy-Dirichlet Problem to Nondiagonal Parabolic Systems with Quadratic Nonlinearities, A.A. Arkhipova Boundary Element Solution of Scattering Problems Relative to a Generalized Impedance Boundary Condition, A. Bendali Mathematical Analysis of Phase-Field Equations with Gradient Coupling Term, M. Benes Qualitative Properties of Positive Solutions of Elliptic Equations, H. Berestycki Nonlinear Boundary Stabilization of the Wave Equation, R. Bey, J.-P. Lohéac, and M. Moussaoui Shape Derivative of Sharp Functionals Governed by Navier-Stokes Flow, S. Boisgérault and J.-P. Zolésio Second Order Shape Derivative for Hyperbolic PDEs, J. Cagnol and J.-P. Zolésio An Axiomatic Approach to image Interpolation, F. Cao, V. Caselles, J.-M. Morel, and C. Sbert A Class of Strong Resonant Problems via Lyapunov-Schmidt Reduction Method, J. Carmona Some Theoretical and Numerical Aspects of Grade-Two Fluid Models, D. Cioranescu, V. Girault, R. Glowinski, and L.R. Scott Large Asymptotic Behavior of Kolmogorov Equations in Hilbert Spaces, G. D a Prato On Existence Results for Fluids with Shear Dependent Viscosity-Unsteady Flows, J. Frehse, J. Målek, and M. Steinhauer Stability of Propagating Fronts in Damped Hyperbolic Equations, Th. Gallay and G. Raugel On the Equations of Melt-Spinning in Viscous Flow, T. Hagen and M. Renardy On Energy Estimates for Electro-Diffusion Equations Arising in Semiconductor Technology, Hünlich and A. Glitzky On the Boundary Conditions at the Contact Interface between Two Porous Media, Jäger and A. Mikelic On the Semistatic Limit for Maxwell's Equations, F. Jochmann Application of Relaxation Schemes and Method of Characteristics to Degenerate Convection-Diffusion Problems, J. Kacur Symmetrization-or How to Prove Symmetry of Solutions to a PDE, B. Kawohl A Bubble-Type Stabilization of the Q1/Q1-Element for Incompressible Flows, P. Knobloch and L