Equadiff 91

(In 2 Volumes)

Proceedings of the International Conference on Differential Equations

International Conference on Differential Equations

, Barcelona, Spain

, 26 – 31 August 1991

https://doi.org/10.1142/1704 | May 1993

Pages: 1032

Edited by:
C Perelló Phua (Universitat Autonoma de Barcelona, Spain),
C Simó (Universitat de Barcelona, Spain), and
J de Solà-Morales (Universitat Politècnica de Catalunya, Spain)

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ISBN: 978-981-4554-71-8 (ebook) USD 316.00 Add to cart

Equadiff-91 stems from the series of conferences initiated by the late Professor Vogel. The first conference Equadiff-70 which was held in Marseille. Since then, similar conferences had been held in Brussels, Florence, Wurzburg as well as Xanthi. The purpose of the Equadiff series of conferences is to present the latest development in the field of differential equations, both ordinary and partial, including their numerical treatment and applications to the mathematics community. These conferences had attracted renowned mathematicians from all over the world to present their studies and findings. The latest conference under the series was Equadiff-91, held in Barcelona. It attracted some 30 renowned mathematicians. Researchers and graduate students of pure and applied mathematics will find this compilation of conference proceedings up-to-date, relevant and insightful.

Contents:

Equilibrium and Dynamics of Bubbles for the Cahn-Hilliard Equation (N D Alikakos & G Fusco)
Simultaneous Normal Form and Center Manifold Reduction for Random Differential Equations (L Arnold & Xu Kedai)
On the Bogdanov-Takens Bifurcation for Planar Diffeomorphisms (H W Broer et al.)
Reasons for a Failure: The Integration of the Two-Body Problem with a Symplectic Runge-Kutta-Nyström Code with Stepchanging Facilities (M P Calvo & J M Sanz-Serna)
Splitting of Separatrices in Rapidly Forced Systems (A Delshams & T M Seara)
On the Impact of the Entropy Function in Computational Fluid Dynamics (by Finite Elements) (L Demkowicz)
On a Conjecture Due to J L Lions Concerning Weak Controllability for Navier-Stokes Flows (E Fernández-Cara & J Real)
Attractors for Dissipative Evolutionary Equations (J K Hale & G Raugel)
Homogenization of Reactive Transport through Porous Media (U Hornung & W Jäger)
Attractors for Nonlinear Parabolic Systems (O Ladyzhenskaya)
Adaptive Least Squares Finite Element Methods for Flow Simulation on Unstructured Grids (K Morgan et al.)
Finite Volume Methods for Modelling the Compressible Navier-Stokes Equations (K W Morton)
On Destruction of Adiabatic Invariants in Multi-Frequency Systems (A Neishtadt)
Monotone Systems and Transversality (W M Oliva)
Non-Conservative Hyperbolic Systems and Two-Phase Flows (P-A Raviart & L Sainsaulieu)
Singular Solutions and Asymptotic Behaviour of Nonlinear Parabolic Equations (J L Vázquez)
and about 150 additional contributions

Readership: Graduates and researchers in pure and applied mathematics.

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Equadiff 91: International Conference on Differential Equations

Pages:1–1036

https://doi.org/10.1142/9789814537438

Preview Abstract

The Table of Contents for the book is as follows:

Volume 1
- Preface
- PLENARY INVITED LECTURES
  - Attractors for Dissipative Evolutionary Equations
  - Attractors for Nonlinear Parabolic Systems
  - Finite Volume Methods for Modelling the Compressible Navier-Stokes Equations
- INVITED LECTURES
  - Equilibrium and Dynamics of Bubbles for the Cahn-Hilliard Equation
  - Simultaneous Normal Form and Center Manifold Reduction for Random Differential Equations
  - On the Bogdanov-Takens Bifurcation for Planar Diffeomorphisms
  - Reasons for a Failure. The Integration of the Two-body Problem with a Symplectic Runge-Kutta-Nyström Code with Stepchanging Facilities
  - Splitting of Separatrices in Rapidly Forced Systems
  - On the Impact of the Entropy Function in Computational Fluid Dynamics (by Finite Elements)
  - On a Conjecture due to J. L. Lions Concerning Weak Controllability for Navier-Stokes Flows
  - Homogenization of Reactive Transport Through Porous Media
  - Solution of Degenerate Parabolic Problems by Linear Approximation Schemes
  - Resurgent Approach to the Separatrices Splitting
  - Periodic Orbits of Periodic Differential Systems
  - Adaptive Least Squares Finite Element Methods for Flow Simulations on Unstructured Grids
  - On Destruction of Adiabatic Invariants in Multi-frequency Systems
  - Monotone Systems and Transversality
  - Dynamics of Scalar Semilinear Parabolic Equations
  - Non-conservative Hyperbolic Systems and Two-phase Flows
  - Singular Solutions and Asymptotic Behaviour of Nonlinear Parabolic Equations
- COMMUNICATIONS
  - Singular Perturbation Analysis of the Coupling of Elliptic and Hyperbolic Differential Equations
  - Finite Element Error Bounds in Spectral Approximations
  - An Analysis of the Uniqueness of the Solutions of the One-dimensional Steady-state Semiconductor Device Equations
  - Geometric of Banach Spaces and Asymptotic and Nonasymptotic Properties of Monotone Equations of Evolution
  - Existence of Periodic Solutions of ODE via Fixed Point Theorems
  - Some Discontinuous Problems
  - Fourth Order Evolution Equations
  - Decay of Solutions for the Equations of Isothermal Gas Dynamics
  - A Note on the Charged Isosceles Three-body Problem
  - Stabilization: The New Look of Stability Theory
  - Exponential Trichotomies and Heteroclinic Orbits
  - An Asymptotic Study Near 4-resonance of Parametric Oscillator with Quadratic Nonlinears
  - High Precision Angles between Invariant Manifolds for Rapidly Forced Hamiltonian Systems
  - A Note on Wave Propagation in Random Media
  - Improved Method of Auxiliary Systems for Quasilinear Difference Equations
  - On Optimal Control Problems for Pseudoparabolic Variational Inequalities
  - Periodic Boundary Value Problems, a Bifurcation Analysis
  - Functional Extension of Gronwall's Inequality and Haar's Lemma
  - Finitely Smooth Linearization of an ODE System near a Hyperbolic Fixed Point
  - A General Approach to the Bifurcation Theory
  - A Nonlinear Model for Size-dependent Population Dynamics
  - On the Self Similar Solutions of the Nonlinear Schrödinger Equation
  - On the Continuation of the Solutions of Lagrange Equations for Holonomic Scleronomic Systems
  - A Green's Formula for Quasilinear Parabolic Operators
  - Knotted Periodic Orbits in Van der Pol Type Equations
  - Cauchy Problem for a Semi Linear Vector Wave Equation
  - Bifurcations in a Predator-prey Model with Memory and Diffusion
  - Integral Criteria for the Asymptotic Behavior of Solutions of Linear Differential Equations — The Duality Principle
  - Bifurcation of Limit Cycles of Quadratic System on the Plane
  - Asymptotic Equivalence of Fundamental Systems of Solutions for Sturm-Liouville Equations
  - Splitting-time and Exponential Fitting-space Discretizations for Diffusion-reaction Problems
  - Singular Limit Cycles for a Class of Differential Equations
  - Persistence of Invariant Tori in Hill's Problem
  - Effective Stability for Nearly Integrable Hamiltonian Systems
  - Functional Differential Equations with Linearly Transformed Arguments and their Applications
  - Existence of Multiple Solutions for First Order Integrodifferential Equations
  - Syzygy Solutions of the Planar Three-body Problem
  - On Boundary Problems for Loaded Equations
  - Connected Branches of Minimal Solutions to Semilinear Elliptic Equations in ℝⁿ
  - On Asymptotic Properties of Solutions of Inhomogeneous Second Order Elliptic Equations in the Exterior of a Bounded Region
  - Solitary Waves and Bücklund Transformation of a Class of Nonlinear Dispersive Dissipative Differential Equations
  - Oscillation of Two-term Differential Equations through Asymptotics
  - The Oblique Derivative Problem for the Case of an Indefinite Weight
  - Normal Forms for Functional Differential Equations and Applications
  - The Existence of Incompressible, Nonconstant Density, Navier-Stokes 3D Flows in Unbounded Domains
  - Oscillations in Difference Equations
  - On a Class of Nonlinear Elliptic Boundary Problems in Unbounded Domains
  - Bogdanov Singularity in the Fitzhugh-Nagumo Equations
Volume 2
- Symplectic Structure vs. Reversibility in the Bifurcation of Periodic Points of Maps
- Oscillation in Delay Differential Equations with Piecewise Constant Arguments
- Application of Global Optimization to Implicit Solution of Partial Differential Equations
- Hopf-zero Bifurcation: Normal Form Calculation and Application to an Electronic Oscillator
- The Frequency Plateaus for a Chain of Forced Oscillators
- On Polynomial Systems with Invariant Algebraic Curves
- Non-existence of Limit Cycles for Some Predator-prey Systems
- Oscillations and Attractivity of Discrete Difference Equation
- Instability of Symmetric Stationary States for Some Nonlinear Schrödinger Equations with an External Magnetic Field
- Global Behaviour of Polynomial Differential Systems in the Positive Orthant
- Dynamics of a Model Equation in Viscoelasticity
- State Transition Matrix of Generalised Linear Differential Systems: A Matrix Pencil Based Approach
- Solutions in Lebesgue Spaces of the Navier-Stokes Equations with Dynamic Boundary Conditions
- Solutions of Prescribed Sign for BVP's with Asymmetric Nonlinearities
- Bornage et Presque-périodicité des Solutions D'Équations Différentielles Dissipatives
- Volterra Integro-differential Inequality and Boundedness Criteria
- Global Existence of Small Solutions to Nonlinear Schrödinger Equations
- Asymptotic Behavior of Solutions of Nonlinear Elliptic Equations with the Critical Sobolev Exponent
- Convergence of Difference Methods for BVPs of Deviated Differential Equations
- Perturbation Formula of Eigenvalues in a Domain with a Thin Handle
- On Quasiperiodic Perturbations of Ordinary Differential Equations near Equilibrium Points
- An Interactive Code to Solve Multipoint Boundary Value Problems
- Moving Sensors for Parabolic Systems
- Bifurcation of Critically Twisted Homoclinic Orbits
- Small Periodic Solutions of Quasilinear Hyperbolic Equations
- Existence and Uniqueness of Limit Cycles for a Special System of Differential Equations on the Plane
- Regularity of Solutions for Quasilinear Parabolic Systems
- Regularity Properties of Parabolic Measures
- Existence of Strong Solutions to Certain Quasilinear Elliptic Problems
- On the Solvability of Dirichlet's Problem for a Class of Nonlinear Elliptic and Parabolic Equations
- On Integral Equations Arising in Numerical-analytic Method of Solving Boundary Value Problems for Differential Functional Equations
- Dynamique de Système de Particules Soumises à des Percussions et au Frottement Sec
- Attractivity and Oscillation for Neutral Equations
- Forced Symmetry Breaking on Hemispheres
- Dirichlet Problem for a Nonlinear Integrodifferential Semiconductor System from n-GaAs Model
- On a Nonlinear Integrodifferential Equation of Parabolic Type
- On the Uniqueness for the Periodic Lotka-Volterra Competition Model with Diffusion
- Continuability of the Solutions of a Differential System without Uniqueness
- Finite and Infinite Dimensional Dynamics Defined by Retarded Functional Differential Equations
- Radial Solutions of Semilinear Elliptic Equations with Prescribed Numbers of Zeros
- About a Fatou Theorem for the p-Laplacian and Related Estimates for the Hausdorff Dimension of the Support of Certain L-harmonic Measures
- Explicit Solution of Coupled Differential-difference Systems Avoiding the Laplace Transform
- Regular Motion in Sitnikov's Problem
- Young Measures: Regularity Results in the Two Well Problem
- Normal Form of Systems of Partial Differential and Pseudo-differential Operators in the Formal Symbol Class and Applications
- Strongly Monotone Skew-product Semidynamical Systems and their Applications in Partial Differential Equations
- On Hamiltonian Structure of Hydrodynamic Type Systems and the Korteweg-de Vries Type Hierarchies
- Singularity Analysis for Two Dimensional Systems with an Oscillatory Forcing
- On the Solvability of the Lamé Equation
- Dynamics on Inertial Manifolds for Reaction-diffusion Systems in a Domain with Thin Channels
- Nonlinear Boundary Value Problem and Inertial Manifold
- An Asymptotic Analysis of Elasticity Problems in Non Compact Domains with Imperfections
- On Partial Stability for Differential Inclusions
- Dual Semigroups Associated with Linear Functional Differential Equations with Infinite Delay
- Asymptotic Behaviour for Large Time of Solutions to Nonlinear Dissipative Evolutional Equations
- A Long-term Integrator Based on Kirchgraber's LISP Code
- Existence and Uniqueness of Stationary Solutions for Viscous Compressible Heat-conductive Fluid with Great Potential and Small Nonpotential Forces
- Critical Growth for a Superlinear Elliptic Problem
- A Model for Aggregating Populations
- Olver's Form Asymptotics for the Localized Solution of the Schrödinger Equation
- The Numerical Approximation of Stiff Systems of ODE's using Iterative Conjugate Gradient Variants
- The Rotation Number of ODE's with a Chessboard Structure
- Stationary Solutions to Infinite Dimensional Stochastic Equations and Nonstandard Analysis
- On the Integrability of Complex Hamiltonian Systems
- Some Remarks on the Singular Problem for the Scalar Parabolic Equation with Variable Diffusion
- Inertial Manifolds, Symmetry and Applications: Dynamics on Thin Domains
- Complex Periodic and Homoclinic Behaviour in an Autonomous Electronic Oscillator
- On a Surjectivity Result for a Superlinear Sturm-Liouville Equation
- A Geometric Condition for a Plane Critical Point to be Globally Asymptotically Stable
- An Elliptic Semilinear Problem Arising in the Undulatory Behaviour of Nonlinear Diffusion Equations
- Existence Theorems for n-th Order Boundary Value Problems
- Two-point BVP for the Equations ẍ = f(t, x)²ⁿ⁺¹ for Large n
- Versal Normal Form and Quadratic Convergence
- Asymptotic Behavior of Solutions of Non-autonomous Scalar Reaction-diffusion Equations
- On the Existence of Wave Trains in Partly Dissipative Systems
- Threshold Delay Differential Equations are Equivalent to Standard FDE's
- L^∞ Stability for Weak Solutions of the Navier-Stokes Equations in ℝ³ with Singular Initial Data
- Quantitative Properties of Solution Sets to Lipschitzean Differential Inclusions
- On Uniform Regularity Estimates and Robust Approximations for Parameter Dependent Problems
- Moduli of Conjugacy in the Triple Collision Collinear Problem
- Kalman's Rank Conditions for Infinite-dimensional Time-dependent Systems
- Controllability Properties for Elliptic Systems
- A Galerkin Type Approximation for Elliptic Problems
- On the Existence of a Polynomial Lyapunov Function
- Pitchfork Interactions in Equivariant Bifurcation Problems
- On “Discontinuous” Boundary Value Problems for Pseudodifferential Operators
- Stability of Some Nonlinear PD Feedback Control Systems
- Product of Operator Semigroups as Solutions of Time-dependent Differential Equations
- Volterra Lattice Wave Trains and the Whitham Method
- A Conically Singular Solution to the Semilinear Wave Equation
- Quasi-stationary Shock Waves for the Modified Burger's Equation
- Problems and Conjectures in the Qualitative Theory of Planar Autonomous Differential Systems
- On the Inversion of Smooth Functions