Applied Nonlinear Analysis

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.

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