# Nonlinear Phenomena in Mathematical Sciences

## 1st Edition

### Proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, Held at the University of Texas at Arlington, Arlington, Texas, June 16–20, 1980

**Editors:**V. Lakshmikantham

**eBook ISBN:**9781483272054

**Imprint:**Academic Press

**Published Date:**28th January 1982

**Page Count:**1062

## Description

Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences.

In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques.

This book will be helpful to students, practitioners, and researchers in the field of mathematics.

## Table of Contents

Contributors

Preface

Honoring Professor Lamberto Cesari

Invited Addresses and Research Reports

Group Properties of un = [f(u)ux]x

Perturbation and Bifurcation in a Discontinuous Nonlinear Eigenvalue Problem

A Singular Fourier Problem with Nonlinear Boundary Condition

Diversity and Spatial Effects on Competitive Systems

A Bang-Bang Type Theorem for Measures

Some Optimal Control Problems for the Helmholtz Equation

Stability of a Large Flexible Beam in Space

Some Constructions in Semi-Dynamical Systems

Identification of Nonlinear Delay Systems Using Spline Methods

Parameter Estimation Techniques for Nonlinear Distributed Parameter Systems

Projection Techniques for Nonlinear Elliptic PDE

An Operational Equation Arising in Synthesis of Optimal Control

The Problem of Graffi-Cesari

A Variational Approach to Solving Semilinear Equations at Resonance

Exchange of Stability and Hopf Bifurcation

Monotone Method for Nonlinear Boundary Value Problems by Linearization Techniques

Existence and Uniqueness of Solutions to Nonlinear-Operator-Differential Equations Generalizing Dynamical Systems of Automatic Spaceship Navigation

A Numerical Method for a Free Surface Density-Driven Flow

Vortex Motions and Their Stability

The Hamilton-Jacobi Equation with an Unbounded Inhomogeneity

Finite Difference Methods for Identification of Hereditary Control Systems

Models of Vertically Transmitted Diseases with Sequential-Continuous Dynamics

Vertically Transmitted Diseases

A Stochastic Compartimentai Model of Preinfarction Angina

A Nonlinear Diffusion System Modelling the Spread of Oro-Faecal Diseases

Existence of Solutions of Hyperbolic Problems

Applications of Differential Inequalities to Gas Lubrication Theory

Comparison Principle and Theory of Nonlinear Boundary Value Problems

Differential Equations with Discontinuous Nonlinearities

An Estimate for the Solution of a Certain Functional Differential Equation of Neutral Type

A Semidiscretization Procedure for Fitzhugh-Nagumo Equations

Bifurcation of Periodic Solutions of Nonlinear Equations in Age-Structured Population Dynamics

Conservation Laws with Dissipation

On Fixed Points of Multivalued Maps

Bifurcation of Stable Periodic Solutions for Periodic Quasilinear Parabolic Equations

Continuity of Weak Solutions to Certain Singular Parabolic Equations

A Problem Arising in the Mathematical Theory of Epidemics

A Collinear A7-Body Problem of Classical Electrodynamics

On Qualitative Properties of Nonlinear Compartmental Systems

The Asymptotic Form of Nonoscillatory Solutions to Fourth-Order Equations

Identification of Nonlinear Compartmental Systems with an Application to the Modelling of the Enzyme Cytochrome P-450

Some Applications of Hadamard's Inverse Function Theorem

Comparison Theorems for Riccati Differential Equations in a B*-Algebra

Oscillations Périodiques des Systèmes Mécaniques Non Lineaires Excitées par des Distributions δ (Percussions) ou δ'

Representation and Asymptotic Behavior of Strongly DampedEvolution Equations

Degree Theoretic Methods in Optimal Control

A Galerkin Numerical Method for a Class of Nonlinear Reaction-Diffusion Systems

On a Semi-Coercive Quasi-Variational Inequality

A Threshold Model of Antigen Antibody Dynamics with Fading Memory

One Phenomenon in Nonlinear Oscillations

Two Fixed Point Principles

Cheap Shooting Methods for Self-Adjoint Problems Using Initial Value Methods

On Entire Solutions in Some Nonlinear Fourth-Order Elliptic Equations

On the Existence of Large Amplitude Plane-Polarized Alfven Waves

Direct Computer Simulation of Nonlinear Waves in Solids, Liquids, and Gases

Functional Equations of Fredholm-Type and Nonlinear Boundary Value Problems

On Structural Identification

Recent Results for Wave Equations of Rayleigh and Van der Pol Type

Group Theoretical Methods and the Nonlinear Schrodinger Equation

Small Deviations from Symmetry in Models in Population Biology

Controllability of Systems which Generate Solvable Lie Algebras and the Associated Problems in Nonlinear Functional Analysis

Positive Solutions of Reaction-Diffusion Systems with Nonlinear Boundary Conditions and the Fixed Point Index

On Bifurcation from Infinity for Positive Solutions on Second-Order Elliptic Eigenvalue Problems

The Principle of Biological Equivalence and Mathematical Modeling in Physiology

A Class of Conservative Methods for the Numerical Solution of Multiphase Stefan Problems

Conjugates of Differential Flows II

Properties of Solutions of Nonlinear Partial Differential Equations Using Finite Element Methods

An Approximation Scheme for Delay Equations

The Center of a Transformation Group

A Priori Bounds in Nonlinear Shell Theory

The Riccati Integral Equation Arising in Optimal Control of Delay Differential Equations

Existence and Asymptotic Behavior of Reaction-Diffusion Systems via Coupled Quasi-Solutions

Emergence of Periodic and Nonperiodic Motions in a Burgers' Channel Flow Model

Nonhomogeneous Boundary Conditions for Generalized Ordinary Differential Subspaces

Weak Continuity and Compactness of Nonlinear Operators

Asymptotic Behavior of the Renewal Equation Arising in the Gurtin Population Model

Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation

Nonlinear Functional Analysis and Periodic Solutions of Semilinear Wave Equations

On Some Semilinear Problems without Compactness

Transformation Techniques and Numerical Solution of Minimax Problems of Optimal Control: Preliminary Results

Bifurcation of Closed Paths from a Closed Path in R2

Local Estimates and the Existence of Multiple Solutions to Nonlinear Elliptic Problems

Sequence of Iterates in Locally Convex Spaces

On Well-Posed and Ill-Posed Extremal Problems

A Nonlinear Volterra Equation in Viscoelasticity

A Model of Whole Muscles Incorporating Functionally Important Nonlinearities

Asymptotic Limit and Blowing-Up Behavior of Solutions for a Reaction-Diffusion System

Large-Scale Eigenmodes of a Turbulent Flat-Plate Boundary Layer

Nonlinear Oscillations in Triggered Systems

Behavior of Solutions of Some Spatially Dependent Integrodifferential Equations

Nonlinear Equations and Passive Networks

A Briot-Bouquet Equation and Subordination

Global Stability of Balanced Predator-Prey Systems

Nonlinear Semigroups, Accretive Operators, and Applications

Activation-Inhibition Patterns

On the Development of an Intrinsic Definition of the Leray-Schauder Degree

Some Recent Developments in the Infinite Time Optimal Control Problem

On Some Nonlinear Problems of Analytical Mechanics and Theory of Stability

Periodic Environments, Harvesting, and a Riccati Equation

A Heuristic Way of Finding Linear Problems from Soliton Solutions of Nonlinear Wave Equations

Existence of Carathéodory-Martin Evolutions

Estimates for Vector-Valued Elliptic-Parabolic Problems of the Second Order

Qualitative Behavior of Ordinary Differential Equations of the Quasilinear and Related Types

On the Existence of Lyapunov Functions in General Systems

Differential Modules and Theorem of Hukuhara-Turrittin

Time-Dependent Integrodifferential Equations in Banach Spaces

Solvability of Nonlinear Odd-Ordered Differential Equations Using K-Monotonicity

Monotonicity and Upper Semicontinuity of Multifunctions

Classification of Certain Continuous Flows

Pharmacokinetic Systems Analysis: Some New Formulations

Functional Difference Equations and an Epidemic Model

Necessary and Sufficient Conditions for Continuous Dependence of Fixed Points of a-Condensing Maps

Differential Inequalities—In Memoriam of Jacek Szarski (1921-1980)

Asymptotic Conditions for Forced Nonlinear Oscillations

Lyapunov Functions for Evolution Equations in Hilbert Spaces via the Operational Riccati Equation

Models of Cell Kinetics and the Estimation of Macromolecular Synthesis Rates

Distributional and Analytic Solutions of Functional Differential Equations

Modeling Cellular Systems and Aging Processes: II. Some Thoughts on Describing an Asynchronously Dividing Cellular System

## Details

- No. of pages:
- 1062

- Language:
- English

- Copyright:
- © Academic Press 1982

- Published:
- 28th January 1982

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483272054

## About the Editor

### V. Lakshmikantham

### Affiliations and Expertise

University of Texas at Arlington, USA