
Applied Nonlinear Analysis
Proceedings of an International Conference on Applied Nonlinear Analysis, Held at the University of Texas at Arlington, Arlington, Texas, April 20–22, 1978
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Applied Nonlinear Analysis contains the proceedings of an International Conference on Applied Nonlinear Analysis, held at the University of Texas at Arlington, on April 20-22, 1978. The papers explore advances in applied nonlinear analysis, with emphasis on reaction-diffusion equations; optimization theory; constructive techniques in numerical analysis; and applications to physical and life sciences. In the area of reaction-diffusion equations, the discussions focus on nonlinear oscillations; rotating spiral waves; stability and asymptotic behavior; discrete-time models in population genetics; and predator-prey systems. In optimization theory, the following topics are considered: inverse and ill-posed problems with application to geophysics; conjugate gradients; and quasi-Newton methods with applications to large-scale optimization; sequential conjugate gradient-restoration algorithm for optimal control problems with non-differentiable constraints; differential geometric methods in nonlinear programming; and equilibria in policy formation games with random voting. In the area of constructive techniques in numerical analysis, numerical and approximate solutions of boundary value problems for ordinary and partial differential equations are examined, along with finite element analysis and constructive techniques for accretive and monotone operators. In addition, the book explores turbulent fluid flows; stability problems for Hopf bifurcation; product integral representation of Volterra equations with delay; weak solutions of variational problems, nonlinear integration on measures; and fixed point theory. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.
Table of Contents
List of Contributors
Preface
Invited Addresses and Research Reports
On Contracting Interval Iteration for Nonlinear Problems in |Rn:|
A Constructive Method for Linear and Nonlinear Stochastic Partial Differential Equations
A Nonlinear Integral and a Bang-Bang Theorem
Optimal Control of Diffusion-Reaction Systems
A Nonlinear Generalization of the Heat Equation Arising in Plasma Physics
Periodic Solutions of Delay Differential Equations Arising in Some Models of Epidemics
Comparison Theorems for Systems of Reaction-Diffusion Equations
Sequential Conjugate Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints
Rotating Spiral Waves and Oscillations in Reaction- Diffusion Equations
Some Applications of Rothe's Method to Parabolic and Related Equations
A Coarse-Resolution Road Map to Methods for Approximating Solutions of Two-Point Boundary-Value Problems
Cone-Valued Periodic Solutions of Ordinary Differential Equations
The Bistable Nonlinear Diffusion Equation: Basic Theory and Some Applications
Product Integral Representation of Solutions to Semilinear Volterra Equations with Delay
Angle-Bounded Operators and Uniqueness of Periodic Solutions of Certain Ordinary Differential Equations
Compartmental Models of Biological Systems: Linear and Nonlinear
New Optimization Problems for Dynamic Multicontroller Decision Theory
Stability Technique and Thought Provocative Dynamical Systems II
Reaction-Diffusion Equations in Abstract Cones
Numerical Solution of Neuromuscular Systems
Separatrices for Dynamical Systems
Stability Problems for Hopf Bifurcation
An Iterative Method for Approximating Solutions to Nonlinear Partial Differential Equations
On the Existence of Invariant Measures
The Role of Direct Feedback in the Cardiac Pacemaker
The Current State of the /V-Body Problem
Stability of McShane Systems
Constructive Techniques for Accretive and Monotone Operators
SUPOR Q: A Boundary Problem Solver for ODEs
Some Recent Developments in Stability of General Systems
On Certain Solutions of an Integrodifferential Equation
A Green's Formula for Weak Solutions of Variational Problems
Application of Fixed Point Theorems in Approximation Theory
Equivalence of Conjugate Gradient Methods and Quasi-Newton Methods
Approximate Solution of Elliptic Boundary-Value Problems by Systems of Ordinary Differential Equations
Asymptotic Behavior of a Class of Discrete-Time Models in Population Genetics
Contributed Papers
The Volume of Distribution in Single-Exit Compartmental Systems
On Identification of Compartmental Systems
Preconditioning for Constrained Optimization Problems with Applications on Boundary-Value Problems
Evaluation of Quasilinear Techniques for Nonlinear Processes with Random Inputs
Two Problems in Nonlinear Finite Element Analysis
Fixed Point Theory and Inwardness Conditions
A Direct Computational Method for Estimating the Parameters of a Nonlinear Model
A Note on the Asymptotic Behavior of Nonlinear Systems
A Second-Stage Eddy-Viscosity Calculation for the Flat-Plate Turbulent Boundary Layer
Nonlinear Optimization and Equilibria in Policy Formation Games with Random Voting
On the Bounded Solutions of a Nonlinear Convolution Equation
Some Unresolved Questions Pertaining to the Mathematical Analysis of Fluorescence Decay Data
Separation and Monotonicity Results for the Roots of the Moment Problem
System Identification of Models Exhibiting Exponential, Harmonic, and Resonant Modes
Differential Equation Algorithms for Minimizing a Function Subject to Nonnegative Constraints
Stability of a Nonlinear Delay Difference Equation in Population Dynamics
Bilinear Approximation and Harmonic Analysis of Analytic Control/Analytic State Systems
Persistent Sets via Lyapunov Functions
Spatial Heterogeneity and the Stability of Predator-Prey Systems: Population Cycles
Cauchy System for the Nonlinear Boundary-Value Problem of a Shallow Arch
A Summary of Recent Experiments to Compute the Topological Degree
Computation of Eigenvalues/Eigenfunctions for Two-Point Boundary-Value Problems
A Continuum Model Appropriate for Nonlinear Analysis of the Solidification of a Pure Metal
Qualitative Dynamics from Asymptotic Expansions
A Second-Stage Eddy-Viscosity Model for Turbulent Fluid Flows: Or a Universal Statistical Tool?
Fixed Point Iterations Using Infinite Matrices
A Numerical Method for Solving the Hamilton-Jacobi Initial Value Problem
Differential Geometric Methods in Nonlinear Programming
Limiting Equations and Total Stability
Product details
- No. of pages: 746
- Language: English
- Copyright: © Academic Press 1979
- Published: January 28, 1979
- Imprint: Academic Press
- eBook ISBN: 9781483272061
About the Editor
V. Lakshmikantham
Affiliations and Expertise
University of Texas at Arlington, USA