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.

chapter 4|11 pages

Qualitative Properties of Positive Solutions of Elliptic Equations

ByH. Berestycki

chapter 5|4 pages

Nonlinear Boundary Stabilization of the Wave Equation

ByR. Bey, J.-P. LohÉac, M. Moussaoui

chapter 6|15 pages

Shape Derivative of Sharp Functionals Governed by Navier-Stokes Flow

ByS. Boisgérault, J.-P. Zolésio

chapter 7|10 pages

Second-Order Shape Derivative for Hyperbolic PDEs

ByJ. Cagnol, J.-P. Zolésio

chapter 8|15 pages

An Axiomatic Approach to Image Interpolation

ByF. Cao, V. Casellers, J.-M. Morel, C. Sbert

chapter 10|12 pages

Some Theoretical and Numerical Aspects of Grade-Two Fluid Models

ByD. Cioranescu, V. Girault, R. Glowinski, L.R. Scott

chapter 11|10 pages

Large Asymptotic Behaviour of Kolmogorov Equations in Hilbert Spaces

ByGiuseppe da Prato

chapter 12|9 pages

On Existence Results for Fluids with Shear Dependent Viscosity - Unsteady Flows

ByJ. Frehse, J. Málek, M. Steinhauer

chapter 13|17 pages

Stability of Propagating Fronts in Damped Hyperbolic Equations

ByT.H. Gallay, G. Raugel

chapter 14|11 pages

On the Equations of Melt-Spinning in Viscous Flow 1

ByT. Hagen, M. Renardy

chapter 16|12 pages

On the Boundary Conditions at the Contact Interface between Two Porous Media

ByW. Jäger, A. Mikelić

chapter 17|12 pages

On the Semistatic Limit for Maxwell’s Equations

ByF. Jochmann

chapter 20|10 pages

A Bubble-Type Stabilization of the Q1/Q1-Element for Incompressible Flows

ByP. Knobloch, L. Tobiska

chapter 21|8 pages

Instability for Incompressible and Inviscid Fluids

ByH. Koch

chapter 22|6 pages

The Kuramoto-Sakaguchi Nonlinear Parabolic Integrodifferential Equation 1

ByMikhail Lavrentiev, R. Spigler

chapter 23|19 pages

Scattering of Acoustical and Electromagnetic Waves by Some Canonical Obstacles

ByE. Meister, A. Passow

chapter 24|10 pages

PDEs, Motion Analysis and 3D Reconstruction from Movies

ByL. Moisan

chapter 26|8 pages

Properties of Optimal Control Problems for Elliptic Equations

ByU. Raitums

chapter 27|11 pages

On the Galerkin Method for Semilinear Parabolic-Ordinary Systems

ByS. Sanfelici

chapter 28|3 pages

Modelling the Dynamic Contact Angle

ByB. Schweizer

chapter 29|10 pages

L1-decay and the Stability of Shock Profiles

ByD. Serre

chapter 31|7 pages

Singularity Formation for the Stefan Problem

ByJ.J.L. Velázquez