Scientific Publications: Giles Auchmuty

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 e-mail to auchmuty@uh.edu for copies or further information.

 A.     Gravitation and Models of Rotating Self-gravitating Fluids.

  1. (with R. Beals), "Models of Rotating Stars", Astrophysical J. May 1, 1971, L79-82.
  2. (with R. Beals), "Variational Solution of some Nonlinear Free Boundary Problems", Archive for Rational Mechanics & Analysis, 43 (1971), 255-271.
  3. "Existence of Axisymmetric Equilibrium Figures", Archive for Rational Mechanics & Analysis, 65, (1977), 249-261.
  4. "Models of Rotating Self-gravitating Liquids", Trends in Applications of Pure Mathematics to Mechanics, Vol.III, (1981), 22-39, Pitman.
  5. "The Global Branching of Rotating Stars", Arch. Rational Mechanics and Analysis, 114, (1991) 179-194.
  6. "An Inequality in Gravitation Theory", SIAM Review, 39, (1997) 127-135.





 B.   Bifurcation Theory, Bifurcating waves and Reaction-Diffusion Equations.
  1. "Lyapunov Methods and Equations of Parabolic Type", Springer Verlag Lecture Notes in Mathematics, Vol. 332, (1973), 1-14.
  2. (with G. Nicolis), "Dissipative Structures, Catastrophes and Pattern Formation: A Bifurcation Analysis", Proc. National Academy of Science, 71, (1974), 2748-2751.
  3. (with G. Nicolis), "Bifurcation Analysis of Reaction-Diffusion Equations, I." Bull. Mathematical Biology, 37, (1975), 323-365.
  4. (with G. Nicolis) "Bifurcation Analysis of Reaction-Diffusion Equations, III. Concentration Oscillations", Bull. Mathematical Biology, 38, (1975), 325-350.
  5. "Positivity for Parabolic and Elliptic Systems", Proc. Royal Society of Edinburgh, 79A, (1977), 183-191.
  6. "Bifurcating Waves", Annals New York Academy of Science, (Proceedings Conference on Bifurcation Theory & its Applications), 316, (1979), 263-278.
  7. "Qualitative Effects of Diffusion in Chemical Systems", Lectures on Mathematics in the Life Sciences, Vol. 10, American Math. Soc. (1978), 49-99.
  8. (with J.C. Alexander), "Global Bifurcation of Waves", Manuscripta Mathematica, 27, (1979), 159-166.
  9. "Bifurcation Analysis of Reaction-Diffusion Equations, IV. Size Dependence", in Instabilites, Bifurcations & Fluctuations in Chemical Systems, (1982), 3-31, U. Texas Press.
  10. "Bifurcation Analysis of Reaction-Diffusion 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), 35-63, Pitman.
  11. (with J.C. Alexander) "Global Bifurcation of Phase-Locked Oscillators", Archive Rational Mechanics & Analysis, 93, (1986) 253-270.
  12. (with J.C. Alexander) "Bifurcation Analysis of Reaction-Diffusion Equations, VI. Multiply Periodic Traveling Waves", SIAM J. Math. Anal. 19, (1988) 100-109.
  13. (with J.G. Alford) "Rotating Wave Solutions of FitzHugh Nagumo Equations", J of Mathematical  Biology, 53, (2006) 797-820.




C.     Div-Curl Boundary Value Problems, Fluid Mechanics and Vector Analysis.
  1. "Bounding Flows in Turbulent Convection", Archive for Rational Mechanics & Analysis, 51, (1973), 228-238.
  2. "Orthogonal Decompositions and Bases for 3-d Vector Fields", Numerical Functional Analysis and Optimization, 15, (1994), 455-488.
  3. "Potential Representations of Incompressible Vector Fields", in Nonlinear Problems in Applied Mathematics, ed Angell et al, SIAM, (1995), 43-49.
  4. "Reconstruction of the Velocity from the Vorticity in 3-d Fluid Flows", Proc. Royal Society London, A454, (1998), 607-630.
  5. (with J.C. Alexander), "L2-well-posedness of Planar div-curl Problems", Archive Rational Mechanics and Analysis 160, (2001), 91-134.
  6. "The Main Inequality of Vector Field Theory", Math. Modeling and Methods in Applied Sciences,  14, (2004) 79-103.  [pdf]
  7. (with J.C. Alexander), "L2-well-posedness of 3d-div-curl Boundary value Problems",  Quarterly of  Applied Mathematics, V63, (2005), 479-508. [pdf]
  8. "Divergence L2-coercivity Inequalities", Numerical Functional Analysis and Applications, 27, (2006), 499-516. [pdf]
  9. "The Stokes Basis for 3d Incompressible Fluid Flows". in Free and Moving Boundaries, Analysis, Simulation and Control, ed R. Glowinski and J-P Zolesio, Lecture Notes in Pure and Applied Mathematics, V 252, Chapman and Hall/CRC (2007), 215-222.  
  10. (with J.C. Alexander), "Finite Energy Solutions of Mixed 3D div-curl Systems", Quarterly of Applied Mathematics, 64, (2006), 335-357. [pdf]
  11. (with P. Kloucek), "Generalized Harmonic Functions and the Dewetting of Thin Films", Applied Functional Analysis and Optimization, 55, (2007), 145-161.





D.     Eigenvalue Problems and Linear Elliptic Boundary Value Problems.
  1. "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 55-72, AMS 1986.
  2. "Unconstrained Variational Principles for Eigenvalues of Real Symmetric Matrices," SIAM J. Applied Math, 20, (1989) 1186-1207.
  3. "Variational Principles for Eigenvalues of Nonsymmetric Matrices," SIAM J. Matrix Anal. & Applns, 10, (1989) 105-117.
  4. "Variational Principles for Eigenvalues of Compact Operators," SIAM J. Applied Math., 20, (1989), 1321-1335.
  5. "Globally, and Rapidly, Convergent Algorithms for Symmetric Eigenvalue Problems", SIAM J. Matrix Anal. and Applications, 12, (1991), 690-706.
  6. (with W.Y. Jia), "Iterative Methods for Hartree Eigenproblems", Mathematical Modeling and Numerical Analysis, 28, (1994), 576-610.
  7. "Variational Principles for Self-Adjoint Elliptic Eigenproblems", in Nonsmooth / Nonconvex Mechanics, ed Gao, Ogden & Stavroulakis, pp 15-42, Kluwer 2001.[pdf]
  8. "Algorithms and Merit Functions for the Principal Eigenvalue", in  Advances in Convex Analysis and Global Optimization, ed Hadjisavvas & Pardolas, Kluwer, (2001), 235-244.
  9. "Steklov Eigenproblems and the Representation of Solutions of Elliptic Boundary Value Problems", Num. Functional Analysis and Optimization, 25, (2004), 321-348.  [pdf]
  10. "Spectral Characterization of the Trace Spaces H^s(bdy)", SIAM J of Math. Anal., 38, (2006) 894-905. [pdf]
  11. "Reproducing Kernels and Hilbert Spaces of Real Harmonic Functions", SIAM J Math Anal., 41, (2009) 1994-2009.
  12. "Bases and Comparison Results for Linear Elliptic Eigenproblems", J. Math. Anal. Appn, 390 (2012), 394-406. see also correction.
  13. (with Q. Han), "Spectral Representations of Solutions of Linear Elliptic Equations on Exterior Regions", J Math Anal Appns 398 (2013), 1-10.
  14. (with Q. Han), "Representations of Solutions of Laplacian Boundary Value Problems on Exterior Regions", Applied Mathematics and Optimization, 69, (2014), 21-45.
  15. (with M. Rivas), "Unconstrained Variational Principles for Linear Elliptic Eigenproblems", submitted.
  16. (with Q. Han), "Well-posedness and Approximation of Solutions of Linear Divergence-form Elliptic Problems on Exterior Regions", submitted






E.     Convex Analysis, Minimax Theory, Nonlinear PDE and  Variational Methods.
  1. "Duality for Non-Convex Variational Principles", J. Differential Equations, 50, (1982), 80-145.
  2. "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 252-260.
  3. "Variational Principles for Operator Equations and Initial Value Problems", J. Nonlinear Analysis, 12, (1988) 531-564.
  4. (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 64-89, Springer Verlag.
  5. "Variational Principles for Variational Inequalities", Nonlinear Funct. Anal. and Optimization, 10, (1989) 863-874.
  6. "Minimax Theorems and Differential Inclusions", Proc. Int. Conference on Differential Equations, Edinburg, Tx., Research Notes in Math Vol 273, (1992), Pitman 6-10.
  7. "Saddle-points and Existence-Uniqueness for Evolution Equations", Differential & Integral Equations, 6, (1993), 1161-1171.
  8. "Min-max Methods for Non-Potential Operator Equations", in Optimization Methods in Partial Differential Equations, ed Cox & Lasiecka, Contemporary Mathematics, Vol 209, American Mathematical Society (1997), 19-28.
  9. "Control-theoretic Methods for Computing Special Solutions of Differential Equations", in Computational Science in the 21st Century, ed Periaux et al. John Wiley (1997), 655-659.
  10. "Variational Principles and Residual Bounds for Non-Potential Equations", Advances in Applied Mathematics and Optimization, ed Gao and Sherali, Springer (2009), 13-24.
  11. "Variational Principles for Initial Value Problems", Contemporary Mathematics V426, AMS (2007) 45-56.
  12. (with Q. Han), "p-Laplacian Boundary Value Problems on Exterior Regions", J. Math Analysis & Applications,
  13. 417, (2014) 260-271.





F.     Algorithms  and  Numerical Simulation.
  1. "The Numerical Solution of the Equations for Rotating Stars", Springer Verlag Lecture Notes in Mathematics, Vol. 430, (1974) 28-60.
  2. "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. 40-44.
  3. "Numerical Calculation of Rotating Stars", Méthodes Numériques en Mathématiques Appliquées, Les Presses de L'Université de Montréal, (1977), 9-26.
  4. "Duality Methods for Non-convex Optimization", Numerical Functional Analysis and Optimization, 10, (1989), 211-264.
  5. "Duality Algorithms for Smooth, Unconstrained Optimization", in Computational Solution of Nonlinear Equations, Proc. Symposia in Applied Mathematics, 26, (1990) AMS, 15-29.
  6. "Globally, and Rapidly, Convergent Algorithms for Symmetric Eigenvalue Problems", SIAM J. Matrix Anal. and Applications, 12, (1991), 690-706.
  7. "A Posteriori Error Estimates for Linear Equations," Numerische Mathematik, 61, (1992), 1-6.
  8. "Lagrangean Variational Principles and Algorithms for the Equilibria of Rotating Self-Gravitating Fluids", Proc. of Conference on Free and Moving Boundary Problems, CMA, Canberra, 30, (1992), 18-41.
  9. "Saddle Point Methods and Algorithms for Solving Non-symmetric Linear Equations", Numer. Functional Anal. & Optimiz. 16, (1995), 1127-1142.
  10. (with C. Zhai), "Computation of Rotating Wave Solutions of Reaction-Diffusion equations on a Circle", East-West J. of Numerical Analysis, 4, (1996), 151-163.





G.     Mathematical Biology, Chemistry and Finance.
  1. (with G. Nicolis), "Dissipative Structures, Catastrophes and Pattern Formation: A Bifurcation Analysis", Proc. National Academy of Science, 71, (1974), 2748-2751.
  2. "Qualitative Effects of Diffusion in Chemical Systems", Lectures on Mathematics in the Life Sciences, Vol. 10, American Math. Soc. (1978), 49-99.
  3. (with W.Y. Lee and R. Rao), "Option Pricing in a lognormal Securities Market with discrete trading", J. Financial Economics, 9, (1981), 75-101.
  4. (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 588-604.
  5. (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 334-358.
  6. (with J. Chadam, E. Merino, P. Ortoleva and E. Ripley) "Moving Redox Fronts and Worm-hole Cave Cascades" Proc. DOE Argonne Conf. on Nonlinear Problems in Energy Research, (1984).
  7. (with 9 coauthors) "Kinetic Modeling of Flow-Reaction Instabilities in Porous Rocks: Application to Uranium Roll Fronts", Proceedings 4th Int. Symp. on Water/rock Interaction, Misasa, Japan, (1984).
  8. (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), 917-934
  9. (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), 87-107.





I.     Inequalities.
  1. (with D. Bao), "Harnack-type Inequalities for Evolution Equations", Proc. American Math. Soc., 122, (1994) 117-130.
  2. (with J. He), "An Integral Inequality in Population Modeling", Solution of problem 95-13, SIAM Review 40, (1998), 710-713.
  3. (with J. He), "An Inequality for Periodic Functions and a Quadratic Imbedding Result", Numerical Functional Analysis and Applications, 21, (2000), 781-789.
  4. "The Main Inequality of Vector Field Theory", Math. Modeling and Methods in Applied Sciences,  14, (2004) 79-103.
  5. "Optimal Coercivity Inequalities in W^(1,p)", Proc. Royal Society of Edinburgh, 135A, (2005), 915-933. 
  6. (with B. Emamizadeh and M. Zivari), "Dependence of Friedrichs' Constant on Boundary Integrals",  Proc. Royal Society Edinburgh, 135A, (2005), 935-939.
  7. "Divergence L2-coercivity Inequalities", Numerical Functional Analysis and Applications, 27, (2006), 499-516.
  8. "Imbeddings and Bounds for Functions with L^q Laplacians", J. Math Anal, Appns, 383, (2011), 25-34. see also the comment .
  9. "Sharp Boundary Trace Inequalities", Proc Royal Soc. Edinburgh, A 144 (2014) 1-12.  



updated April 12th, 2014.