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

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. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv LIST OF CONTRIBUTORS, Pages xiii-xviii PREFACE, Pages xix-xx ON CONTRACTING INTERVAL ITERATION FOR NONLINEAR PROBLEMS IN : I, Pages 3-11, E. Adams, W.F. Ames A CONSTRUCTIVE METHOD FOR LINEAR AND NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS, Pages 13-23, G. Adomian A NON LINEAR INTEGRAL AND A BANG-BANG THEOREM, Pages 25-46, Richard A. Alo, T. Alvager, Andre de Korvin OPTIMAL CONTROL OF DIFFUSION-REACTION SYSTEMS, Pages 47-59, H.T. Banks, M.C. Duban, J.P. Kernevez A NONLINEAR GENERALIZATION OF THE HEAT EQUATION ARISING IN PLASMA PHYSICS, Pages 61-66, Charles J. Holland, James G. Berryman PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS ARISING IN SOME MODELS OF EPIDEMICS, Pages 67-78, Stavros N. Busenberg, Kenneth L. Cooke COMPARISON THEOREMS FOR SYSTEMS OF REACTION-DIFFUSION EQUATIONS, Pages 79-87, Jagdish Chandra, Paul Wm. Davis SEQUENTIAL CONJUGATE GRADIENT-RESTORATION ALGORITHM FOR OPTIMAL CONTROL PROBLEMS WITH NONDIFFERENTIAL CONSTRAINTS, Pages 89-93, A. Miele, J.R. Cloutier ROTATING SPIRAL WAVES AND OSCILLATIONS IN REACTION-DIFFUSION EQUATIONS, Pages 95-109, Donald S. Cohen SOME APPLICATIONS OF ROTHE'S METHOD TO PARABOLIC AND RELATED EQUATIONS, Pages 111-121, C. Covduneanu A COARSE-RESOLUTION ROAD MAP TO METHODS FOR APPROXIMATING SOLUTIONS OF TWO-POINT BOUNDARY-VALUE PROBLEMS, Pages 123-126, James W. Daniel CONE-VALUED PERIODIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS, Pages 127-142, Klaus Deimling THE BISTABLE NONLINEAR DIFFUSION EQUATION: BASIC THEORY AND SOME APPLICATIONS, Pages 143-160, Paul C. Fife PRODUCT INTEGRAL REPRESENTATION OF SOLUTIONS TO SEMILINEAR VOLTERRA EQUATIONS WITH DELAY, Pages 161-173, W.E. Fitzgibbon ANGLE-BOUNDED OPERATORS AND UNIQUENESS OF PERIODIC SOLUTIONS OF CERTAIN ORDINARY DIFFERENTIAL EQUATIONS, Pages 175-183, Chaitan P. Gupta COMPARTMENTAL MODELS OF BIOLOGICAL SYSTEMS: LINEAR AND NONLINEAR, Pages 185-205, John A. Jacquez NEW OPTIMIZATION PROBLEMS FOR DYNAMIC MULTICONTROLLER DECISION THEORY, Pages 207-213, Harriet Kagiwada STABILITY TECHNIQUE AND THOUGHT PROVOCATIVE DYNAMICAL SYSTEMS II, Pages 215-218, G.S. Ladde REACTION-DIFFUSION EQUATIONS IN ABSTRACT CONES, Pages 219-243, V. Lakshmikantham, A.S. Vatsala, S. Leela NUMERICAL SOLUTION OF NEURO-MUSCULAR SYSTEMS, Pages 245-266, K.V. Leung, M.N. Oğuztöreli, R.B. Stein SEPARATRICES FOR DYNAMICAL SYSTEMS, Pages 267-271, Roger C. McCann STABILITY PROBLEMS FOR HOPF BIFURCATION, Pages 273-286, P. Negrini, L. Salvadori AN ITERATIVE METHOD FOR APPROXIMATING SOLUTIONS TO NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, Pages 287-297, J.W. Neuberger ON THE EXISTENCE OF INVARIANT MEASURES, Pages 299-307, Giulio Pianigiani THE ROLE OF DIRECT FEEDBACK IN THE CARDIAC PACEMAKER, Pages 309-321, Richard E. Plant THE CURRENT STATE OF THE N-BODY PROBLEM, Pages 323-324, Harry Pollard STABILITY OF McSHANE SYSTEMS, Pages 325-333, A.N.V. Rao, C.P. Tsokos CONSTRUCTIVE TECHNIQUES FOR ACCRETIVE AND MONOTONE OPERATORS, Pages 335-345, Simeon Reich SUPOR Q: A BOUNDARY PROBLEM SOLVER FOR ODE's, Pages 347-350, M.R. Scott, H.A. Watts SOME RECENT DEVELOPMENTS IN STABILITY OF GENERAL SYSTEMS, Pages 351-371, Peter Seibert ON CERTAIN SOLUTIONS OF AN INTEGRODIFFERENTIAL EQUATION, Pages 373-380, George Seifert A GREEN's FORMULA FOR WEAK SOLUTIONS OF VARIATIONAL PROBLEMS, Pages 381-387, R.E. Showalter APPLICATION OF FIXED POINT THEOREMS IN APPROXIMATION THEORY, Pages 389-394, S.P. Singh EQUIVALENCE OF CONJUGATE GRADIENT METHODS AND QUASI-NEWTON METHODS, Page 395, R.A. Tapia APPROXIMATE SOLUTION OF ELLIPTIC BOUNDARY VALUE PROBLEMS BY SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS, Pages 397-405, Russell C. Thompson ASYMPTOTIC BEHAVIOR OF A CLASS OF DISCRETE-TIME MODELS IN POPULATION GENETICS, Pages 407-422, H.F. Weinberger THE VOLUME OF DISTRIBUTION IN SINGLE-EXIT COMPARTMENTAL SYSTEMS, Pages 425-437, David H. Anderson ON IDENTIFICATION OF COMPARTMENTAL SYSTEMS, Pages 439-448, S. Sandberg, D.H. Anderson, J. Eisenfeld PRECONDITIONING FOR CONSTRAINED OPTIMIZATION PROBLEMS WITH APPLICATIONS ON BOUNDARY VALUE PROBLEMS, Pages 449-450, Owe Axelsson EVALUATION OF QUASI-LINEAR TECHNIQUES FOR NONLINEAR PROCESSES WITH RANDOM INPUTS, Pages 451-466, M. Balakrishna, David A. Hullender TWO PROBLEMS IN NONLINEAR FINITE ELEMENT ANALYSIS, Pages 467-477, G.F. Carey, T.T. Pan, R. Renka FIXED POINT THEORY AND INWARDNESS CONDITIONS, Pages 479-483, James Caristi A DIRECT COMPUTATIONAL METHOD FOR ESTIMATING THE PARAMETERS OF A NONLINEAR MODEL, Pages 485-497, Stephen W. Cheng, Jerome Eisenfeld A NOTE ON THE ASYMPTOTIC BEHAVIOR OF NONLINEAR SYSTEMS, Pages 499-505, Kuo-Liang Chiou A SECOND-STAGE EDDY-VISCOSITY CALCULATION FOR THE FLAT-PLATE TURBULENT BOUNDARY LAYER, Pages 507-517, Sue-Li Chuang, Fred R. Payne NONLINEAR OPTIMIZATION AND EQUILIBRIA IN POLICY FORMATION GAMES WITH RANDOM VOTING, Pages 519-527, Peter Coughlin ON THE BOUNDED SOLUTIONS OF A NONLINEAR CONVOLUTION EQUATION, Pages 529-530, Odo Diekmann, Hans G. Kaper SOME UNRESOLVED QUESTIONS PERTAINING TO THE MATHEMATICAL ANALYSIS OF FLUORESCENCE DECAY DATA, Pages 531-542, Corey C. Ford, Jerome Eisenfeld SEPARATION AND MONOTONICITY RESULTS FOR THE ROOTS OF THE MOMENT PROBLEM, Pages 543-553, James Hallmark, Jerome Eisenfeld SYSTEM IDENTIFICATION OF MODELS EXHIBITING EXPONENTIAL, HARMONIC AND RESONANT MODES, Pages 555-568, B. Soni, J. Eisenfeld DIFFERENTIAL EQUATION ALGORITHMS FOR MINIMIZING A FUNCTION SUBJECT TO NONNEGATIVE CONSTRAINTS, Pages 569-575, B.S. Goh STABILITY OF A NONLINEAR DELAY DIFFERENCE EQUATION IN POPULATION DYNAMICS, Pages 577-585, B.S. Goh BILINEAR APPROXIMATION AND HARMONIC ANALYSIS OF ANALYTIC CONTROL/ANALYTIC STATE SYSTEMS, Pages 587-604, R.D.S. Grisell PERSISTENT SETS VIA LYAPUNOV FUNCTIONS, Pages 605-606, G.W. Harrison SPATIAL HETEROGENEITY AND THE STABILITY OF PREDATOR-PREY SYSTEMS: POPULATION CYCLES, Pages 607-618, Alan Hastings CAUCHY SYSTEM FOR THE NONLINEAR BOUNDARY VALUE PROBLEM OF A SHALLOW ARCH, Pages 619-625, R.E. Kalaba, E.A. Zagustin A SUMMARY OF RECENT EXPERIMENTS TO COMPUTE THE TOPOLOGICAL DEGREE, Pages 627-633, Baker Kearfott COMPUTATION OF EIGENVALUES/EIGENFUNCTIONS FOR TWO POINT BOUNDARY VALUE PROBLEMS, Pages 635-656, M.E. Lord, M.R. Scott, H.A. Watts A CONTINUUM MODEL APPROPRIATE FOR NONLINEAR ANALYSIS OF THE SOLIDIFICATION OF A PURE METAL, Pages 657-668, David J. Wollkind, Ronald D. Notestine, Robert N. Maurer QUALITATIVE DYNAMICS FROM ASYMPTOTIC EXPANSIONS, Pages 669-673, J.A. Murdock A SECOND STAGE EDDY-VISCOSITY MODEL FOR TURBULENT FLUID FLOWS: OR, A UNIVERSAL STATISTICAL TOOL?, Pages 675-688, Fred R. Payne FIXED POINT ITERATIONS USING INFINITE MATRICES, Pages 689-703, K.L. Singh A NUMERICAL METHOD FOR SOLVING THE HAMILTON-JACOBI INITIAL VALUE PROBLEM, Pages 705-706, Michael Tamburro DIFFERENTIAL GEOMETRIC METHODS IN NONLINEAR PROGRAMMING, Pages 707-719, Kunio Tanabe LIMITING EQUATIONS AND TOTAL STABILITY, Pages 721-726, F. Visentin On contracting interval iteration for nonlinear problems in IR:I; 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 - difusion 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; Cone-valued periodic solutions of ordinary differential equations; The bistable nonlinear diffusion equation: basic theory and some apllications; Product integral representations of solutions to semilinear volterra equations with delay; Angle-bounded operators and uniqueness of periodic solutions of certain ordinary differential equations; Comportamental 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 n-body problem; Stability of McShane systems; Constructive techniques for accretive and monotone operators; 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 thorems 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; The volume of distribution in single-exit compartmental systems; Preconditioning for constrained optimization problems with applications on boun 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