Proceedings of
Dynamic Systems and Applications


Volume 1

CONTENTS

Preface
N. U. Ahmed
Functional analysis on Wiener measure space and evolutions on Fock
spaces
1


V. Alexiades and G. K. Jacobs
Solidification modeling of In Situ Vitrification melts
11

J.C. Angeles-Fernandez and H. G. Gonzalez Hernandez
Sim-Caos: A non-linear dynamics simulator
17

Abdelkader Boucherif
Periodic boundary value problems with Caratheodory nonlinearities
25

Baruch Cahlon
On the numerical stability of Volterra integral equations with and without
delay
33


Yulin Cao and Thomas C. Gard
Population interaction models with continuous time delays
43

C.Y. Chan
Quenching phenomena for reaction-diffusion equations
51

C.Y. Chan and L. Ke
Remarks on impulsive quenching problems
59

C.Y. Chan and P. C. Kong
Effects of degenerate parabolic operators on quenching and beyond
quenching
63


C. Y. Chan and N. Ozalp
Singular parabolic mixed boundary-value problems
69

Gary Chung
Minimum time null controllability of duffing oscillator
73

Gary Chung and N. Medhin
Optimality conditions for functional differential control systems
81

R. DeVault, E.A. Grove, G. Ladas, R. Levins and C. Puccia
Oscillation and stability in models of a perennial grass
87

M. L. Frankal and V. Roytburd
Dynamics of thermal instability
95

Kenneth Gilliam and Carlos Vinante
Variable structure control with first order plus integral sliding conditions
103

Jose M. Gonzalez
Dynamics of the population inside a functional economic area (FEA)
111

John R. Graef and Paul W. Spikes
Some results on the asymptotic behavior of solutions of a nonlinear
difference equation with a forcing term
121


Jong-Sheng Guo
The Competition between fast diffusion and source
127

Yung_Jen Guo and Walter Littman
The null boundary controllability for semilinear heat equations
135

Seppo Heikkila
On extremal solutions of infinite systems of discontinuous differential
equations
143


Leighton Izu
Cardiac calcium oscillations in a diffusion equation with nonlinear
boundary conditions
151


Billur Kaymakcalan and Lalitha Rangarajan
Variation of Lyapunov's method for dynamic systems on time scales
159

V. B. Kolmanovskii and L. Shaikhet
New results in stability theory for stochastic functional differential
equations(SFDEs) and their applications
167


G. E. Kolosov
Approximate method for design of stochastic adaptive optimal control
systems
173


S. V. Krishna
Control by impulse, delay and history
181

G. S. Ladde, S. Sathananthan and M. V. Moorthy
Periodic boundary value problems for second order integro-differential
equations of Volterra type
191


V. Lakshmikantham
Monotone iterative technique for discontinuous differential systems
199

V. Lakshmikantham and S. Koksal
Another extension of the method of quasilinearization
205

Irena Lasiecka
Compact attractors for Von Karman equations with nonlinear boundary
damping
211


J. Lopez-Gomez and R. Pardo
On the uniqueness and stability of coexistence states for some predator-prey
models with diffusion
221


J. Lopez-Gomez and J. C. Sabina De Lis
Dynamics of competing species models
229

M. Lopez-Rodriguez and C. E. Billigheimer
The nested-circle theorem for differential operator on some commutative
B*-algebras
237


N. G. Medhin and M. Sambandham
Numerical solution of boundary value problems
245

Ronald Mickens
Genesis of elementary numerical instabilities in finite-difference models
of ordinary differential equations
251


Stephen W. Mohn and E.Bruce Lee
Elastic beam control: precision shape deformations
259

John Mooney
Existence and critical parameters in the solution of semilinear singular
parabolic problems
265


A. S. Muleshkov and C. S. Chen
A note on the critical lengths for mixed boundary value problems
271

George Osipenko
Localization of the chain recurrent set by symbolic dynamics methods
277

Daniel Phillips
Remarks on vortices in nonlinear heat flow
283

Alexander G. Ramm
Multidimensional inverse scattering: solved and unsolved problems
287

Zvi Retchkiman
The disturbance decoupling problem for nonlinear systems and its
relation to the solution of certain kind of partial differential equations
297


Abdulalim A Shabazz
Generalizations of two well-known results on Hermitian forms
301

D.J. Shippy and H. Fu
Bifurcations and chaos of a parametrically excited pendulum
307

Angela Slavova
Constructive method for solving nonlinear singularly perturbed systems
315

M. W. Smiley
Numerical computation of certain approximate inertial manifolds
323

K. Sriskandarajah
Global bifurcation of a sinusoidally forced duffing equation
331

Lev Steinberg
Inverse problems for free oscillations of cylinders and bars
335

Tory Story
Characteristic electromagnetic and Yang-Mills gauge
343

Suzanne Sumner
Competing species models for pioneer-climax forest dynamical systems
351

Antonio Tineo
Three dimensional periodic systems with trivial dynamics
359

Sheung Tsun Tsou
A topological variation problem in quantum field theory
365

A. S. Vatsala
Stability results of nonlocal reaction diffusion systems via vector
Lyapunov functions
371


Kehong Wen, Ping Chen, and Jack S. Turner
Bifurcation in a Lienard equation with two delays
377

Patricia J. Y. Wong and Ravi P. Agarwal
Existence and uniqueness of solutions of higher order boundary
value problems
385


D. T. Wu
Stability of the approximate solution of SOIE
393

G. Yin
Integral equations with random perturbations arose from
stochastic approximations
399


Eutiquio C. Young and Hongzheng Xie
A normal mode solution of an underwater acoustic problem
407

Qingxin Zhu and N. U. Ahmed
Some results on Hamilton-Jacobi-Bellman equations in Banach space
415

Editors
423
Speakers
424