Ebook: Dynamics of Infinite Dimensional Systems

The 1986 NATO Advanced Study Insti tute on Dynamics of Infini te Dimensional Systems was held at the Instituto Superior Tecnico. Lisbon. Portugal. In recent years. there have been several research workers who have been considering partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications. the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come wi th several different backgrounds - some from classical partial differential equations. some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Workshop was to bring together research workers from these various areas. It provided asoundboard for the impact of the ideas of each respective discipline. We believe that goal was accomplished. but time will be a better judge. We have included the list of participants at the workshop. with most of these giving a presentation. Although the proceedings do not include all of the presentations. it is a good representative sampie. We wish to express our gratitude to NATO. and.to Dr. M. di Lullo of NATO. who unfortunately did not live to see the completion of this project.

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This volume presents the results of a NATO Advanced Study Institute on Dynamics of Infinite Dimensional Systems, held at the Instituto Superior Tecnico, Lisbon, Portugal, May 19-24, 1986. In recent years several research workers have considered partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications, the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come from different backgrounds - some from classical partial differential equations, some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Institute was to bring together research workers from these various areas. It provided a soundboard for the impact of the ideas of each respective discipline.

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This volume presents the results of a NATO Advanced Study Institute on Dynamics of Infinite Dimensional Systems, held at the Instituto Superior Tecnico, Lisbon, Portugal, May 19-24, 1986. In recent years several research workers have considered partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications, the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come from different backgrounds - some from classical partial differential equations, some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Institute was to bring together research workers from these various areas. It provided a soundboard for the impact of the ideas of each respective discipline.
Content:
Front Matter....Pages I-IX
Semilinear Parabolic Systems Under Nonlinear Boundary Conditions....Pages 1-6
The Shadowing Lemma for Elliptic PDE....Pages 7-22
Coagulation-Fragmentation Dynamics....Pages 23-30
Functional Differential Equations and Jensen’s Inequality....Pages 31-38
Method of Upper and Lower Solutions for Nonlinear Integral Equations and an Application to an Infectious Disease Model....Pages 39-44
Competition of Azimuthal Modes and Quasi-Periodic Flows in the Couette-Taylor Problem....Pages 45-56
On Bifurcation for Variational Problems....Pages 57-60
Nilpotent Normal Form in Dimension 4....Pages 61-66
Perturbed Dual Semigroups and Delay Equations....Pages 67-73
On Operators Which Leave Invariant a Half-Space....Pages 75-80
Global Hopf Bifurcation in Reaction Diffusion Systems with Symmetry....Pages 81-104
Longtime Behavior for a Class of Abstract Integrodifferential Equations....Pages 105-111
Describing the Flow on the Attractor of One Dimensional Reaction Diffusion Equations by Systems of ODE....Pages 113-121
Asymptotic Behavior of Gradient Dissipative Systems....Pages 123-128
Generic Properties of Equilibrium Solutions by Perturbation of the Boundary....Pages 129-139
Complex Analytical Methods in RFDE Theory....Pages 141-149
Qualitative Behavior of the Solutions of Periodic First Order Scalar Differential Equations with Strictly Convex Coercive Nonlinearity....Pages 151-159
The Spectrum of Invariant Sets for Dissipative Semiflows....Pages 161-168
Approximate Solutions to Conservation Laws Via Convective Parabolic Equations : Analytical and Numerical Results....Pages 169-177
Conley’s Connection Matrix....Pages 179-186
Existence and Non-Existence of Finite-Dimensional Globally Attracting Invariant Manifolds in Semilinear Damped Wave Equations....Pages 187-210
SLEP Method to the Stability of Singularly Perturbed Solutions with Multiple Internal Transition Layers in Reaction-Diffusion Systems....Pages 211-230
Iterated Nonlinear Maps and Hilbert’s Projective Metric: A Summary....Pages 231-248
Jacobi Matrices and Transversality....Pages 249-255
Examples of Attractors in Scalar Reaction-Diffusion Equations....Pages 257-272
Gauge Theory of Backlund Transformations, I....Pages 273-300
Recent Developments in the Theory of Nonlinear Scalar First and Second Order Partial Differential Equations....Pages 301-311
Hopf Bifurcation for an Infinite Delay Functional Equation....Pages 313-323
A Numerical Analysis of the Structure of Periodic Orbits in Autonomous Functional Differential Equations....Pages 325-339
Oscillations and Asymptotic Behaviour for Two Semilinear Hyperbolic Systems....Pages 341-356
An Application of the Conley Index to Combustion....Pages 357-372
Path Continuation — A Sensitivity Analysis Approach....Pages 373-383
Confinor and Anti-confinor in Constrained “Lorenz” System....Pages 385-407
Invariant Manifolds in Infinite Dimensions....Pages 409-420
Linearizing Completely Integrable Systems on Complex Algebraic Tori....Pages 421-449
On Some Dynamical Aspects of Parabolic Equations with Variable Domain....Pages 451-457
Bifurcation from Homoclinic to Periodic Solutions by an Inclination Lemma with Pointwise Estimate....Pages 459-470
Approximate Methods for Set Valued Differential Equations with Delays....Pages 471-479
Bounds for the Chaotic Behavior of Newton’s Method....Pages 481-510
Back Matter....Pages 511-516

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This volume presents the results of a NATO Advanced Study Institute on Dynamics of Infinite Dimensional Systems, held at the Instituto Superior Tecnico, Lisbon, Portugal, May 19-24, 1986. In recent years several research workers have considered partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications, the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come from different backgrounds - some from classical partial differential equations, some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Institute was to bring together research workers from these various areas. It provided a soundboard for the impact of the ideas of each respective discipline.
Content:
Front Matter....Pages I-IX
Semilinear Parabolic Systems Under Nonlinear Boundary Conditions....Pages 1-6
The Shadowing Lemma for Elliptic PDE....Pages 7-22
Coagulation-Fragmentation Dynamics....Pages 23-30
Functional Differential Equations and Jensen’s Inequality....Pages 31-38
Method of Upper and Lower Solutions for Nonlinear Integral Equations and an Application to an Infectious Disease Model....Pages 39-44
Competition of Azimuthal Modes and Quasi-Periodic Flows in the Couette-Taylor Problem....Pages 45-56
On Bifurcation for Variational Problems....Pages 57-60
Nilpotent Normal Form in Dimension 4....Pages 61-66
Perturbed Dual Semigroups and Delay Equations....Pages 67-73
On Operators Which Leave Invariant a Half-Space....Pages 75-80
Global Hopf Bifurcation in Reaction Diffusion Systems with Symmetry....Pages 81-104
Longtime Behavior for a Class of Abstract Integrodifferential Equations....Pages 105-111
Describing the Flow on the Attractor of One Dimensional Reaction Diffusion Equations by Systems of ODE....Pages 113-121
Asymptotic Behavior of Gradient Dissipative Systems....Pages 123-128
Generic Properties of Equilibrium Solutions by Perturbation of the Boundary....Pages 129-139
Complex Analytical Methods in RFDE Theory....Pages 141-149
Qualitative Behavior of the Solutions of Periodic First Order Scalar Differential Equations with Strictly Convex Coercive Nonlinearity....Pages 151-159
The Spectrum of Invariant Sets for Dissipative Semiflows....Pages 161-168
Approximate Solutions to Conservation Laws Via Convective Parabolic Equations : Analytical and Numerical Results....Pages 169-177
Conley’s Connection Matrix....Pages 179-186
Existence and Non-Existence of Finite-Dimensional Globally Attracting Invariant Manifolds in Semilinear Damped Wave Equations....Pages 187-210
SLEP Method to the Stability of Singularly Perturbed Solutions with Multiple Internal Transition Layers in Reaction-Diffusion Systems....Pages 211-230
Iterated Nonlinear Maps and Hilbert’s Projective Metric: A Summary....Pages 231-248
Jacobi Matrices and Transversality....Pages 249-255
Examples of Attractors in Scalar Reaction-Diffusion Equations....Pages 257-272
Gauge Theory of Backlund Transformations, I....Pages 273-300
Recent Developments in the Theory of Nonlinear Scalar First and Second Order Partial Differential Equations....Pages 301-311
Hopf Bifurcation for an Infinite Delay Functional Equation....Pages 313-323
A Numerical Analysis of the Structure of Periodic Orbits in Autonomous Functional Differential Equations....Pages 325-339
Oscillations and Asymptotic Behaviour for Two Semilinear Hyperbolic Systems....Pages 341-356
An Application of the Conley Index to Combustion....Pages 357-372
Path Continuation — A Sensitivity Analysis Approach....Pages 373-383
Confinor and Anti-confinor in Constrained “Lorenz” System....Pages 385-407
Invariant Manifolds in Infinite Dimensions....Pages 409-420
Linearizing Completely Integrable Systems on Complex Algebraic Tori....Pages 421-449
On Some Dynamical Aspects of Parabolic Equations with Variable Domain....Pages 451-457
Bifurcation from Homoclinic to Periodic Solutions by an Inclination Lemma with Pointwise Estimate....Pages 459-470
Approximate Methods for Set Valued Differential Equations with Delays....Pages 471-479
Bounds for the Chaotic Behavior of Newton’s Method....Pages 481-510
Back Matter....Pages 511-516
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