Applied Nonlinear Analysis

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

1st Edition - January 28, 1979

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  • Editor: V. Lakshmikantham
  • eBook ISBN: 9781483272061

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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


    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

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