SCIENTIFIC PUBLICATIONS
:
The publications below
are arranged by subject
area. Some papers are
listed under more than one
heading. Reprints of most
of the following papers
are available from the
author. Send email to
auchmuty@uh.edu for copies
or further information.
A. Gravitation
and Models of Rotating
Selfgravitating
Fluids.
B. Bifurcation
Theory, Bifurcating
waves and
ReactionDiffusion
Equations.
C. DivCurl
Boundary Value
Problems, Fluid
Mechanics and Vector
Analysis.
D. Linear
Elliptic Boundary
Value Problems and
Function Spaces.
E. Eigenvalue
problems and
Variational
Principles.
F. Variational
Principles, Duality
and Saddlepoint
problems.
G. Inequalities.
H.
Numerical
Methods and
algorithms.
I. Mathematical
Biology, Chemistry and
Finance.
Also view my Recent
publications
A.
Gravitation
and Models of Rotating
Selfgravitating Fluids.
 (with R. Beals),
"Models of Rotating
Stars", Astrophysical J.
May 1, 1971, L7982.
 (with R. Beals),
"Variational Solution of
some Nonlinear Free
Boundary Problems",
Archive for Rational
Mechanics &
Analysis, 43 (1971),
255271.
 "Existence of
Axisymmetric Equilibrium
Figures", Archive for
Rational Mechanics &
Analysis, 65, (1977),
249261.
 "Models of Rotating
Selfgravitating
Liquids", Trends in
Applications of Pure
Mathematics to
Mechanics, Vol.III,
(1981), 2239, Pitman.
 "The Global Branching
of Rotating Stars",
Arch. Rational Mechanics
and Analysis, 114,
(1991) 179194.
 "An Inequality in
Gravitation Theory",
SIAM Review, 39, (1997)
127135.
B.
Bifurcation Theory,
Bifurcating waves and
ReactionDiffusion
Equations.
 "Lyapunov Methods and
Equations of Parabolic
Type", Springer Verlag
Lecture Notes in
Mathematics, Vol. 332,
(1973), 114.
 (with G. Nicolis),
"Dissipative Structures,
Catastrophes and Pattern
Formation: A Bifurcation
Analysis", Proc.
National Academy of
Science, 71, (1974),
27482751.
 (with G. Nicolis),
"Bifurcation Analysis of
ReactionDiffusion
Equations, I." Bull.
Mathematical Biology,
37, (1975), 323365.
 (with G. Nicolis)
"Bifurcation Analysis of
ReactionDiffusion
Equations, III.
Concentration
Oscillations", Bull.
Mathematical Biology,
38, (1975), 325350.
 "Positivity for
Parabolic and Elliptic
Systems", Proc. Royal
Society of Edinburgh,
79A, (1977), 183191.
 "Bifurcating Waves",
Annals New York Academy
of Science, (Proceedings
Conference on
Bifurcation Theory &
its Applications), 316,
(1979), 263278.
 "Qualitative Effects
of Diffusion in Chemical
Systems", Lectures on
Mathematics in the Life
Sciences, Vol. 10,
American Math. Soc.
(1978), 4999.
 (with J.C.
Alexander), "Global
Bifurcation of Waves",
Manuscripta Mathematica,
27, (1979), 159166.
 "Bifurcation Analysis
of ReactionDiffusion
Equations, IV. Size
Dependence", in
Instabilites,
Bifurcations &
Fluctuations in Chemical
Systems, (1982), 331,
U. Texas Press.
 "Bifurcation Analysis
of ReactionDiffusion
Equations, V. Rotating
Waves on A Disc" in
Partial Differential
Equations and Dynamical
Systems, ed. W.E.
Fitzgibbon, Research
Notes in Mathematics,
Vol. 101, (1984), 3563,
Pitman.
 (with J.C. Alexander)
"Global Bifurcation of
PhaseLocked
Oscillators", Archive
Rational Mechanics &
Analysis, 93, (1986)
253270.
 (with J.C. Alexander)
"Bifurcation Analysis of
ReactionDiffusion
Equations, VI. Multiply
Periodic Traveling
Waves", SIAM J. Math.
Anal. 19, (1988)
100109.
 (with J.G. Alford)
"Rotating Wave Solutions
of FitzHugh Nagumo
Equations", J of
Mathematical
Biology, 53, (2006)
797820.
C.
DivCurl
Boundary Value Problems,
Field Theory and
Fluid Mechanics.
 "Bounding Flows in
Turbulent Convection",
Archive for Rational
Mechanics &
Analysis, 51, (1973),
228238.
 "Orthogonal
Decompositions and Bases
for 3d Vector Fields",
Numerical Functional
Analysis and
Optimization, 15,
(1994), 455488.
 "Potential
Representations of
Incompressible Vector
Fields", in Nonlinear
Problems in Applied
Mathematics, ed
Angell et al, SIAM,
(1995), 4349.
 "Reconstruction of
the Velocity from the
Vorticity in 3d Fluid
Flows", Proc. Royal
Society London, A454,
(1998), 607630.
 (with J.C.
Alexander),
"L2wellposedness of
Planar divcurl
Problems", Archive
Rational Mechanics and
Analysis 160, (2001),
91134.
 "The Main Inequality
of Vector Field Theory",
Math. Modeling and
Methods in Applied
Sciences, 14,
(2004) 79103.
[pdf]
 (with J.C. Alexander),
"L2wellposedness of
3ddivcurl Boundary
value Problems",
Quarterly of
Applied Mathematics,
V63, (2005), 479508.
 "Divergence
L2coercivity
Inequalities", Numerical
Functional Analysis and
Applications, 27,
(2006), 499516.
 "The Stokes Basis for
3d Incompressible Fluid
Flows". in Free and
Moving Boundaries,
Analysis, Simulation and
Control, ed R. Glowinski
and JP Zolesio, Lecture
Notes in Pure and
Applied Mathematics, V
252, Chapman and
Hall/CRC (2007),
215222.
 (with J.C. Alexander),
"Finite Energy Solutions
of Mixed 3D divcurl
Systems", Quarterly of
Applied Mathematics, 64,
(2006), 335357.
 (with P. Kloucek),
"Generalized Harmonic
Functions and the
Dewetting of Thin
Films", Applied
Mathematics and
Optimization, 55,
(2007), 145161.
 (with D. R. Simpkins),
"Spectral
Representations and
Approximations of
Divergencefree Vector
Fields", Quarterly of
Applied Math. 74, (2016)
429441.
 "Electrostatic
Approximation of Vector
Fields", to appear in
"System Modeling and
Optimization", ed Bociu,
Desideri and Habal,
Springer. [pdf]
 "Bounds and Regularity
of Solutions of Planar
DivCurl Problems",
Quarterly of Applied
Mathematics 75, (2007),
50252.
D.
Linear Elliptic
Boundary Value Problems
and Function Spaces.
 "Steklov Eigenproblems
and the Representation
of Solutions of Elliptic
Boundary Value
Problems", Num.
Functional Analysis and
Optimization, 25,
(2004), 321348.
 "Spectral
Characterization of the
Trace Spaces H^s(bdy)",
SIAM J of Math. Anal.,
38, (2006) 894905.
 "Reproducing Kernels
and Hilbert Spaces of
Real Harmonic
Functions", SIAM J
Math Analysis, 41 (2009)
19942009.
 "Finite energy
solutions of
Selfadjoint Elliptic
Mixed Boundary Value
Problems",
Mathematical Methods in
the Applied Sciences.
33, (2010) 14461462.
 "Imbeddings and Bounds
for Functions with L^q
Laplacians", J. Math
Anal and Applications,
383, (2011) 2534. see
also this
correction.
 (with P. Kloucek),
"Spectral solutions of
Selfadjoint Elliptic
Problems with Immersed
Interfaces", Applied
Mathematics and
Optimization, 64.
(2011), 311338.
 (with Qi Han),
"Spectral Representation
of Solutions of Linear
Elliptic Equations on
Exterior Regions", J.
Math. Anal & Appns,
(361), 2013, 110.
 (with Qi Han),
"Representations of
Solutions of Laplacian
Boundary Value Problems
on Exterior Regions",
Applied Math &
Optimization, 69 (2014),
2145.
 (with Q. Han),
"pLaplacian Boundary
Value Problems on
Exterior Regions", J.
Math Anal Appns 417,
(2014), 260271..
 (with Q. Han),
""Wellposedness and
approximation of
solutions of linear
divergenceform elliptic
problems on exterior
regions", Math Methods
in the Applied Sciences,
38, (2015), 18671875.
 (with M. Cho),
"Boundary Integrals and
Approximations of
Harmonic Functions",
Numerical functional
Analysis and
Applications, 36,
(2015), 687703.
 (with M.A. Rivas),
"Laplacian Eigenproblems
on Product Regions and
Tensor Products of
Hilbert Spaces", J.
Math. Anal & Appns,
435, (2016), 842859 and
this
addendum
 "The S.V.D. of the
Poisson Kernel", J.
Fourier Analysis and
Applications, November
2016, pp 120 see
http://rdcu.be/mEqr
DOI:
10.1007/s0004101695155
 "Steklov
Representations of
Green's Functions for
Laplacian Boundary Value
Problems", Applied
Mathematics and
Optimization (to
appear). DOI:
10.1007/s0024501693704
pp 123. [.pdf]
E.
Eigenvalue
Problems
 "Dual Variational
Principles for
Eigenvalue Problems" in
Nonlinear Functional
Analysis and its
Applications (ed. F.E.
Browder), Proc. Symposia
in Pure Mathematics,
Vol. 45, Part 1, pp
5572, AMS 1986.
 "Unconstrained
Variational Principles
for Eigenvalues of Real
Symmetric Matrices,"
SIAM J. Applied Math,
20, (1989) 11861207.
 "Variational
Principles for
Eigenvalues of
Nonsymmetric Matrices,"
SIAM J. Matrix Anal.
& Applns, 10, (1989)
105117.
 "Variational
Principles for
Eigenvalues of Compact
Operators," SIAM J.
Applied Math., 20,
(1989), 13211335.
 "Globally, and
Rapidly, Convergent
Algorithms for Symmetric
Eigenvalue Problems",
SIAM J. Matrix Anal. and
Applications, 12,
(1991), 690706.
 (with W.Y. Jia),
"Iterative Methods for
Hartree Eigenproblems",
Mathematical Modeling
and Numerical Analysis,
28, (1994), 576610.
 "Variational
Principles for
SelfAdjoint Elliptic
Eigenproblems", in
Nonsmooth / Nonconvex
Mechanics, ed Gao, Ogden
& Stavroulakis, pp
1542, Kluwer 2001.[pdf]
 "Algorithms and Merit
Functions for the
Principal Eigenvalue",
in Advances in
Convex Analysis and
Global Optimization, ed
Hadjisavvas
& Pardolas,
Kluwer, (2001), 235244.
 "Steklov Eigenproblems
and the Representation
of Solutions of Elliptic
Boundary Value
Problems", Num.
Functional Analysis and
Optimization, 25,
(2004), 321348.
 "Bases and Comparison
Results for Linear
Elliptic Eigenproblems".
J. Math Anal and
Applications, 390,
(2012) 394406.
See corrections
here.
 (with M. Rivas),
"Unconstrained
Variational Principles
for Linear Elliptic
Eigenproblems," ESIAM
Control and
Calculus of Variations,
21, (2015), 165189.
F.
Inequalities.
 (with D. Bao),
"Harnacktype
Inequalities for
Evolution Equations",
Proc. American Math.
Soc., 122, (1994)
117130.
 (with J. He), "An
Integral Inequality in
Population Modeling",
Solution of problem
9513, SIAM Review 40,
(1998), 710713.
 (with J. He), "An
Inequality for Periodic
Functions and a
Quadratic Imbedding
Result", Numerical
Functional Analysis and
Applications, 21,
(2000), 781789.
 "The Main Inequality
of Vector Field Theory",
Math. Modeling and
Methods in Applied
Sciences, 14,
(2004) 79103.
[pdf]
 "Optimal Coercivity
Inequalities in
W^(1,p)", Proc. Royal
Society of Edinburgh,
135A, (2005),
915933.
 (with B. Emamizadeh
and M. Zivari),
"Dependence of
Friedrichs' Constant on
Boundary
Integrals", Proc.
Royal Society Edinburgh,
135A, (2005),
935939.
 "Divergence
L2coercivity
Inequalities", Numerical
Functional Analysis and
Applications, 27,
(2006), 499516.
 "Parametric Dependence
of Boundary Trace
Inequalities," Proc Conf
on Differential and
Difference Equations,
Springer Proceedings in
Math. and Statistics,
Vol 47, 249254.
 "Sharp Boundary Trace
Inequalities",
Proceedings Royal
Society of Edinburgh A,
144 (2014), 1 12.
>>
Back to Top
G.
Convex Analysis, Minimax
Theory and
Variational Methods.
 "Duality for
NonConvex Variational
Principles", J.
Differential Equations,
50, (1982), 80145.
 "Variational
Principles for Periodic
Solutions of Autonomous
Ordinary Differential
Equations", in Nonlinear
Oscillations in
Chemistry and Biology,
Lecture Notes in
Biomathematics, Vol. 66,
(1986) Springer Verlag
pp 252260.
 "Variational
Principles for Operator
Equations and Initial
Value Problems", J.
Nonlinear Analysis, 12,
(1988) 531564.
 (with E. Dean, R.
Glowinski and S.C.
Zhang) "Optimal Control
Methods for finding
Periodic Solutions of
Differential Equations"
in "Control Problems for
Systems Described by
Partial Differential
Equations and
Applications," ed. I.
Lasiecka and R.
Triggiani, Lecture Notes
in Control and
Information Science,
Vol. 97, (1987), pp
6489, Springer Verlag.
 "Variational
Principles for
Variational
Inequalities", Nonlinear
Funct. Anal. and
Optimization, 10, (1989)
863874.
 "Minimax Theorems and
Differential
Inclusions", Proc. Int.
Conference on
Differential Equations,
Edinburg, Tx., Research
Notes in Math Vol 273,
(1992), Pitman 610.
 "Saddlepoints and
ExistenceUniqueness for
Evolution Equations",
Differential &
Integral Equations, 6,
(1993), 11611171.
 "Minmax Methods for
NonPotential Operator
Equations", in Optimization
Methods in Partial
Differential Equations,
ed Cox & Lasiecka,
Contemporary
Mathematics, Vol 209,
American Mathematical
Society (1997), 1928.
 "Controltheoretic
Methods for Computing
Special Solutions of
Differential Equations",
in Computational
Science in the 21st
Century, ed
Periaux et al. John
Wiley (1997), 655659.
 "Variational
Principles and Residual
Bounds for NonPotential
Equations", in Advances
in Applied Mathematics
and Global Optimization,
ed d.Y. Gao and H.D.
Sherali, Vol 17,
Advances in Mechanics
and Mathematics,
Springer (2009), 1323.
 "Variational
Principles for Initial
Value Problems",
Contemporary Mathematics
V426, AMS (2007) 4556
with addendum here .[pdf]
H.
Algorithms,
Approximations
and Numerical
Simulation.
 "The Numerical
Solution of the
Equations for Rotating
Stars", Springer Verlag
Lecture Notes in
Mathematics, Vol. 430,
(1974) 2860.
 "Numerical Models of
Rotating Stars",
Springer Verlag Lecture
Notes in Physics, Vol.
35, Proceedings of the
Fourth International
Conference on Numerical
Methods in Fluid
Dynamics (1975) pp.
4044.
 "Numerical
Calculation of Rotating
Stars", Méthodes
Numériques en
Mathématiques
Appliquées, Les Presses
de L'Université de
Montréal, (1977), 926.
 "Duality Methods for
Nonconvex
Optimization", Numerical
Functional Analysis and
Optimization, 10,
(1989), 211264.
 "Duality Algorithms
for Smooth,
Unconstrained
Optimization", in
Computational Solution
of Nonlinear Equations,
Proc. Symposia in
Applied Mathematics, 26,
(1990) AMS, 1529.
 "Globally, and
Rapidly, Convergent
Algorithms for Symmetric
Eigenvalue Problems",
SIAM J. Matrix Anal. and
Applications, 12,
(1991), 690706.
 "A Posteriori Error
Estimates for Linear
Equations," Numerische
Mathematik, 61, (1992),
16.
 "Lagrangean
Variational Principles
and Algorithms for the
Equilibria of Rotating
SelfGravitating
Fluids", Proc. of
Conference on Free and
Moving Boundary
Problems, CMA, Canberra,
30, (1992), 1841.
 "Saddle Point Methods
and Algorithms for
Solving Nonsymmetric
Linear Equations",
Numer. Functional Anal.
& Optimiz. 16,
(1995), 11271142.
 (with C. Zhai),
"Computation of Rotating
Wave Solutions of
ReactionDiffusion
equations on a Circle",
EastWest J. of
Numerical Analysis, 4,
(1996), 151163.
 (with M. Cho),
"Boundary Integrals and
Approximations of
Harmonic Functions",
Numerical Functional
Analysis & Appns,
36, (2015) 687703.
 (with Douglas
Simpkins), "Spectral
Representations and
Approximations of
Divergencefree Vector
Fields", Quarterly of
Applied Mathematics 74,
(2016), 429441.
13.
"Electrostatic
Approximation of Vector
Fields", to appear in
"System Modeling and
Optimization", ed Bociu,
Desideri and Habal,
Springer.
14. (with M.
Cho), "Steklov
Approximations of Harmonic
Boundary Value Problems",
J. of Computational &
Applied Matheatics, 321,
(2017) 302313.
I.
Mathematical
Biology, Chemistry and
Finance.
 (with G. Nicolis),
"Dissipative Structures,
Catastrophes and Pattern
Formation: A Bifurcation
Analysis", Proc.
National Academy of
Science, 71, (1974),
27482751.
 "Qualitative Effects
of Diffusion in Chemical
Systems", Lectures on
Mathematics in the Life
Sciences, Vol. 10,
American Math. Soc.
(1978), 4999.
 (with W.Y. Lee and R.
Rao), "Option Pricing in
a lognormal Securities
Market with discrete
trading", J. Financial
Economics, 9, (1981),
75101.
 (with J. Chadam, E.
Merino, P. Ortoleva and
E. Ripley) "The
Structure and Stability
of Propagating Redox
Fronts", SIAM J. of
Applied Math, 46,
(1986), pp 588604.
 (with P. Ortoleva, J.
Chadam, J. Hettmer, E.
Merino, C. Moore and E.
Ripley), "Redox Front
Propagation and Banding
Modalities", Physica D.
19D (1986), pp 334358.
 (with J. Chadam, E.
Merino, P. Ortoleva and
E. Ripley) "Moving Redox
Fronts and Wormhole
Cave Cascades" Proc. DOE
Argonne Conf. on
Nonlinear Problems in
Energy Research, (1984).
 (with 9 coauthors)
"Kinetic Modeling of
FlowReaction
Instabilities in Porous
Rocks: Application to
Uranium Roll Fronts",
Proceedings 4th Int.
Symp. on Water/rock
Interaction, Misasa,
Japan, (1984).
 (with M.N.
Obeyesekere, E.S.
Tecarro and S.O.
Zimmerman), "A model of
cell cycle behavior
dominated by kinetics of
a pathway stimulated by
growth factors", Bull.
Math. Biology, 61,
(1999), 917934
 (with M.N.
Obeyesekere and E.S.
Tecarro), "Analysis of a
model of the Mammalian
Cell cycle's G1 phase",
Nonlinear Analysis and
Applications, Real World
Applications, 4, (2003),
87107.
updated August
2017.
