Partial Differential Equations

Theory and Numerical Solution

J. Necas, Willi Jager, Jana Stara, Oldrich John, Karel Najzar

• Publisher: Routledge
• Year: 2018
• Print ISBN:
  9781584880226
  9780367834661
• Edition: 1
• eBook ISBN:
  9781351425865
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

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.

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• On the Global in Time Solvability of the Cauchy-Dirichlet Problem to Nondiagonal Parabolic Systems with Quadratic Nonlinearities
• Boundary Element Solution of Scattering Problems Relative to a Generalized Impedance Boundary Condition
• Mathematical Analysis of Phase-Field Equations with Gradient Coupling Term
• Qualitative Properties of Positive Solutions of Elliptic Equations
• Nonlinear Boundary Stabilization of the Wave Equation
• Shape Derivative of Sharp Functionals Governed by Navier-Stokes Flow
• Second-Order Shape Derivative for Hyperbolic PDEs
• An Axiomatic Approach to Image Interpolation
• A Class of Strong Resonant Problems via Lyapunov-Schmidt Reduction Method
• Some Theoretical and Numerical Aspects of Grade-Two Fluid Models
• Large Asymptotic Behaviour of Kolmogorov Equations in Hilbert Spaces
• On Existence Results for Fluids with Shear Dependent Viscosity – Unsteady Flows
• Stability of Propagating Fronts in Damped Hyperbolic Equations
• On the Equations of Melt-Spinning in Viscous Flow
• On Energy Estimates for Electro-Diffusion Equations Arising in Semiconductor Technology
• On the Boundary Conditions at the Contact Interface between Two Porous Media
• On the Semistatic Limit for Maxwell’s Equations
• Application of Relaxation Schemes and Method of Characteristics to Degenerate Convection-Diffusion Problems
• Symmetrization or How to Prove Symmetry of Solutions to a PDE
• A Bubble–Type Stabilization of the Q1/Q1–Element for Incompressible Flows
• Instability for Incompressible and Inviscid Fluids
• The Kuramoto–Sakaguchi Nonlinear Parabolic Integrodifferential Equation
• Scattering of Acoustical and Electromagnetic Waves by Some Canonical Obstacles
• PDEs, Motion Analysis and 3D Reconstruction from Movies
• Steady Flow of Viscoelastic Fluid Past an Obstacle — Asymptotic Behaviour of Solutions
• Properties of Optimal Control Problems for Elliptic Equations
• On the Galerkin Method for Semilinear Parabolic-Ordinary Systems
• Modelling the Dynamic Contact Angle
• L1-decay and the Stability of Shock Profiles
• On Positive Solutions of the Equation ΔU + f(|x|)UP = 0 in Rn, n > 2
• Singularity Formation for the Stefan Problem
• On the Construction of Interior Spike Layer Solutions to a Singularly Perturbed Semilinear Neumann Problem