Graeme Wake

Articles in Scholarly Journals [Incomplete List]

  1. Long-term coexistence for a competitive system of spatially varying gradient reaction–diffusion equations
    Nonlinear Analysis: Real World Applications, vol. 10, no. 1, pp. 93–103, 2009
  2. A mathematical model for pollution in a river and its remediation by aeration
    Applied Mathematics Letters, 2008
  3. The steady-states of a multi-compartment, age–size distribution model of cell-growth
    European Journal of Applied Mathematics, vol. 19, no. 04, 2008
  4. A mollified method for the solution of the Cauchy problem for the convection-diffusion equation
    Inverse Problems in Science and Engineering, vol. 15, no. 4, pp. 293–302, 2007
  5. Solutions of inverse problems with potential application for breast tumour detection using microwave measurements
    Computational and Mathematical Methods in Medicine, vol. 8, no. 4, pp. 245–261, 2007
  6. Statistics and Applied Probability: A Tribute to Jeffrey J. Hunter
    Journal of Applied Mathematics and Decision Sciences, vol. 2007, Article ID 57619, 4 pages, 2007
  7. Self-heating in compost piles due to biological effects
    Chemical Engineering Science, vol. 62, no. 17, pp. 4612–4619, 2007
  8. A bifurcation analysis of a simple phytoplankton and zooplankton model
    Mathematical and Computer Modelling, vol. 45, no. 3-4, pp. 449–458, 2007
  9. The distribution of urine deposited on a pasture from grazing animals
    The Journal of Agricultural Science, vol. 145, no. 01, p. 81, 2007
  10. Ecological pricing and transformity: A solution method for systems rarely at general equilibrium
    Ecological Economics, vol. 56, no. 3, pp. 412–423, 2006
  11. A lattice Boltzmann-based model of plankton–flow interaction around a mussel cluster
    Ecological Modelling, vol. 192, no. 3-4, pp. 645–657, 2006
  12. On a functional equation model of transient cell growth
    Mathematical Medicine and Biology, vol. 22, no. 4, pp. 371–390, 2005
  13. Targeted Glycemic Reduction in Critical Care Using Closed-Loop Control
    Diabetes Technology Therapeutics, vol. 7, no. 2, pp. 274–282, 2005
  14. Impact of control on agitation–sedation dynamics
    Control Engineering Practice, vol. 13, no. 9, pp. 1139–1149, 2005
  15. Modelling the flow of cytometric data obtained from unperturbed human tumour cell lines: parameter fitting and comparison
    Bulletin of Mathematical Biology, vol. 67, no. 4, pp. 815–830, 2005
  16. Erratum to “Modelling the flow cytometric data obtained from unperturbed human tumour cell lines: parameter fitting and comparison” [Bull. Math. Biol. 67 (2005) 815–830]
    Bulletin of Mathematical Biology, vol. 67, no. 5, pp. 1153–1153, 2005
  17. Adaptive bolus-based targeted glucose regulation of hyperglycaemia in critical care
    Medical Engineering & Physics, vol. 27, no. 1, pp. 1–11, 2005
  18. The existence of steady states to a combustion model with internal heating
    Nonlinear Analysis: Real World Applications, vol. 5, no. 3, pp. 421–439, 2004
  19. Modelling cell population growth with applications to cancer therapy in human tumour cell lines
    Progress in Biophysics and Molecular Biology, vol. 85, no. 2-3, pp. 353–368, 2004
  20. Analysis of a predator–prey system with predator switching
    Bulletin of Mathematical Biology, vol. 66, no. 1, pp. 109–123, 2004
  21. Minimal haemodynamic system model including ventricular interaction and valve dynamics
    Medical Engineering & Physics, vol. 26, no. 2, pp. 131–139, 2004
  22. Modeling and control of the agitation–sedation cycle for critical care patients
    Medical Engineering & Physics, vol. 26, no. 6, pp. 459–471, 2004
  23. A natural boundary for solutions to the second order pantograph equation
    Journal of Mathematical Analysis and Applications, vol. 299, no. 2, pp. 314–321, 2004
  24. Holomorphic solutions to pantograph type equations with neutral fixed points
    Journal of Mathematical Analysis and Applications, vol. 295, no. 2, pp. 557–569, 2004
  25. Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel
    Journal of Mathematical Biology, vol. 49, no. 4, pp. 329–357, 2004
  26. An Eigenvalue problem for holomorphic solutions to a certain class of functional differential equations
    European Journal of Applied Mathematics, vol. 14, no. 5, pp. 571–585, 2003
  27. A mathematical model for analysis of the cell cycle in cell lines derived from human tumors
    Journal of Mathematical Biology, vol. 47, no. 4, pp. 295–312, 2003
  28. Core bulk of wool fibres as a function of their curvature and diameter
    Physics Letters A, vol. 314, no. 5-6, pp. 428–433, 2003
  29. Analysis of a class of distributed delay logistic differential equations
    Mathematical and Computer Modelling, vol. 38, no. 1-2, pp. 123–132, 2003
  30. The evolution of a truncated gaussian probability density through time?modelling animal liveweights after selection
    Mathematical and Computer Modelling, vol. 38, no. 11-13, pp. 1461–1468, 2003
  31. Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models
    Applied Mathematics Letters, vol. 15, no. 8, pp. 955–960, 2002
  32. Influence of Milking Frequency on Mammary Gland Dynamics
    Journal of Theoretical Biology, vol. 218, no. 4, pp. 521–530, 2002
  33. A delay model for the growth of ryegrass–clover mixtures: formulation and preliminary simulations
    Ecological Modelling, vol. 155, no. 1, pp. 31–42, 2002
  34. Natural Boundaries for Solutions to a Certain Class of Functional Differential Equations
    Journal of Mathematical Analysis and Applications, vol. 268, no. 1, pp. 157–170, 2002
  35. Active insulin infusion using optimal and derivative-weighted control
    Medical Engineering & Physics, vol. 24, no. 10, pp. 663–672, 2002
  36. Banded chaos in power systems
    IEEE Transactions on Power Delivery, vol. 16, no. 1, pp. 105–110, 2001
  37. On a singular Sturm-Liouville problem involving an advanced functional differential equation
    European Journal of Applied Mathematics, vol. 12, no. 06, p. 625, 2001
  38. Variational methods for boundary value problems
    Journal of Applied Mathematics and Decision Sciences, vol. 4, no. 2, pp. 193–204, 2000
  39. Heterogeneously catalysed combustion in a continuously stirred tank reactor—low-temperature reactions
    Combustion Theory and Modelling, vol. 4, no. 1, pp. 1–27, 2000
  40. Analysis of the impact of stoats, Mustela erminea, on northern brown kiwi, Apteryx mantelli, in New Zealand
    Wildlife Research, vol. 26, no. 2, p. 227, 1999
  41. Modelling spontaneous combustion in wet lignite
    Combustion Theory and Modelling, vol. 3, no. 2, pp. 215–232, 1999
  42. Global properties of the three-dimensional predator-prey Lotka-Volterra systems
    Journal of Applied Mathematics and Decision Sciences, vol. 3, no. 2, pp. 155–162, 1999
  43. A dynamical systems model of the interaction of earthworms with plant litter quality and quantity
    Agricultural Systems, vol. 59, no. 1, pp. 27–39, 1999
  44. Radiative ignition of combustible materials I. Polymeric materials undergoing nonflaming thermal degradation?the critical storage problem*1
    Mathematical and Computer Modelling, vol. 30, no. 11-12, pp. 177–195, 1999
  45. Critical initial conditions for spontaneous thermal ignition
    Journal of the Chemical Society, Faraday Transactions, vol. 94, no. 24, pp. 3613–3617, 1998
  46. Analysis of the bifurcational behaviour of a simple model of vapour ignition in porous material
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 453, no. 1957, pp. 281–301, 1997
  47. Multiple solutions in hollow geometries in the theory of thermal ignition
    Applied Mathematics Letters, vol. 10, no. 5, pp. 41–46, 1997
  48. Theory and use of functionals on the class of nonnegative polynomials and quadrature formulae
    Mathematical and Computer Modelling, vol. 25, no. 6, pp. 45–55, 1997
  49. Modelling pasture mass through time in a managed grazing system subject to perturbations resulting from complexity in natural biological processes
    Agricultural Systems, vol. 53, no. 2-3, pp. 191–208, 1997
  50. Critical values for some non-class A geometries in thermal ignition theory
    Mathematical and Computer Modelling, vol. 24, no. 8, pp. 1–10, 1996
  51. Gel'fand's equation in spherical domains: II. Further results and the spherical annulus revisited
    Mathematical and Computer Modelling, vol. 24, no. 8, pp. 47–54, 1996
  52. Revisiting spontaneous ignition of solids with diminishing reaction rates
    AIChE Journal, vol. 42, no. 8, pp. 2388–2391, 1996
  53. The relaxation of May's conjecture for the logistic equation
    Applied Mathematics Letters, vol. 9, no. 5, pp. 59–62, 1996
  54. Self-ignition of solids with diminishing reaction rates. Exact comparison between the results predicted using time-dependent and surface-oxygen absorption-dependent reaction rate
    Journal of the Chemical Society, Faraday Transactions, vol. 92, no. 16, p. 2977, 1996
  55. The ignition of combustible material in the presence of a damp atmosphere
    Physics Letters A, vol. 191, no. 1-2, pp. 61–70, 1994
  56. The regulation of a dispersive age-structured population by a fatal disease
    Applied Mathematics Letters, vol. 7, no. 4, pp. 79–83, 1994
  57. A differential-delay model of pasture accumulation and loss in controlled grazing systems
    Mathematical Biosciences, vol. 121, no. 1, pp. 37–60, 1994
  58. Path-following for disjoint bifurcation problems arising in ignition theory
    Mathematical and Computer Modelling, vol. 19, no. 9, pp. 9–15, 1994
  59. A simple model for optimizing rotational grazing
    Agricultural Systems, vol. 41, no. 2, pp. 123–155, 1993
  60. Critical initial conditions for thermal ignition
    Mathematical and Computer Modelling, vol. 18, no. 8, pp. 65–75, 1993
  61. Multiplicity of solutions of a quasilinear elliptic equation in spherical domains
    Mathematical and Computer Modelling, vol. 18, no. 10, pp. 157–162, 1993
  62. Comparison Theorems for Coupled Reaction-Diffusion Equations in Chemical Reactor Analysis
    Journal of Mathematical Analysis and Applications, vol. 178, no. 1, pp. 196–220, 1993
  63. The self-heating of damp cellulosic materials: II. On the steady states of the spatially distributed case
    IMA Journal of Applied Mathematics, vol. 50, no. 3, pp. 285–306, 1993
  64. The self-heating of damp cellulosic materials: I. High thermal conductivity and diffusivity
    IMA Journal of Applied Mathematics, vol. 49, no. 3, pp. 273–291, 1992
  65. Outputs and time lags for linear bioreactors
    Mathematical and Computer Modelling, vol. 16, no. 12, pp. 109–120, 1992
  66. The prediction of a practical lower bound for ignition delay times and a method of scaling times-to-ignition in large reactant masses from laboratory data-II
    Symposium (International) on Combustion, vol. 24, no. 1, pp. 1785–1791, 1992
  67. A simple method for obtaining good bounds for solutions of reaction-diffusion equations with nonlinear kinetics
    Chemical Engineering Science, vol. 46, no. 1, pp. 49–55, 1991
  68. Disjoint bifurcation diagrams in combustion systems
    Mathematical and Computer Modelling, vol. 15, no. 11, pp. 25–33, 1991
  69. Multiplicity of steady state solutions for combustion in a solid sphere with arbitrary Biot number
    Physics Letters A, vol. 153, no. 1, pp. 16–20, 1991
  70. Picoplankton and marine food chain dynamics in a variable mixed-layer: a reaction-diffusion model
    Ecological Modelling, vol. 57, no. 3-4, pp. 193–219, 1991
  71. Heat Conduction and Finite Measures for Transition Times between Steady States
    IMA Journal of Applied Mathematics, vol. 47, no. 2, pp. 193–206, 1991
  72. Inverse Problems, vol. 7, no. 4, pp. 633–642, 1991
  73. Mathematical Analysis: An Inverse Problem Arising in Convective-Diffusive Flow
    IMA Journal of Applied Mathematics, vol. 45, no. 3, pp. 225–231, 1990
  74. Effect of deposition of combustible matter onto electric power cables
    Fire Safety Journal, vol. 16, no. 6, pp. 459–467, 1990
  75. The ignition of hygroscopic combustible materials by water
    Combustion and Flame, vol. 79, no. 1, pp. 2–6, 1990
  76. The dynamics of a model of a plankton-nutrient interaction
    Bulletin of Mathematical Biology, vol. 52, no. 5, pp. 677–696, 1990
  77. A numerical scheme for solving a stream nutrient model
    Applied Mathematical Modelling, vol. 13, no. 3, pp. 155–159, 1989
  78. Determination of Critical Ambient Temperatures for Thermal Ignition
    IMA Journal of Applied Mathematics, vol. 42, no. 2, pp. 147–154, 1989
  79. Addendum to ‘On the Existence and Stability of Spatially Structured Solutions of the Reaction-Diffusion Equations‘
    IMA Journal of Applied Mathematics, vol. 40, no. 2, pp. 145–146, 1988
  80. On the determination of critical ambient temperatures and critical initial temperatures for thermal ignition
    Combustion and Flame, vol. 71, no. 1, pp. 101–104, 1988
  81. On the Existence and Stability of Spatially Structured Solutions of the Reaction-Diffusion Equations
    IMA Journal of Applied Mathematics, vol. 37, no. 1, pp. 25–35, 1986
  82. Theory of Thermal Explosions with Simultaneous Parallel Reactions. II. The Two- and Three-Dimensional Cases and the Variational Method
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990), vol. 401, no. 1820, pp. 195–202, 1985
  83. Friction and localized heat initiation of ignition: The asymmetrical slab and cylindrical annulus
    Combustion and Flame, vol. 61, no. 2, pp. 177–187, 1985
  84. Criticality in the infinite slab and cylinder with surface heat sources
    Combustion and Flame, vol. 55, no. 1, pp. 23–30, 1984
  85. Existence of solutions to a nonlinear boundary value problem by variational means
    Journal of Mathematical Analysis and Applications, vol. 92, no. 2, pp. 581–598, 1983
  86. Stokes Flow Between Parallel Plates due to a Trausversely Moving End Wall
    IMA Journal of Applied Mathematics, vol. 30, no. 2, pp. 141–149, 1983
  87. Thermal Ignition with Variable Thermal Conductivity
    IMA Journal of Applied Mathematics, vol. 28, no. 1, pp. 23–39, 1982
  88. The disappearance of criticality for small activation energy with arbitrary biot number
    Combustion and Flame, vol. 45, pp. 287–291, 1982
  89. On the disappearance of criticality in the theory of thermal ignition
    ZAMP Zeitschrift f�r angewandte Mathematik und Physik, vol. 33, no. 3, pp. 406–407, 1982
  90. Criticality in a model for thermal ignition in three or more dimensions
    ZAMP Zeitschrift f�r angewandte Mathematik und Physik, vol. 32, no. 5, pp. 594–602, 1981
  91. The disappearance of criticality in the theory of thermal ignition
    Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 29, no. 6, pp. 971–976, 1978
  92. The dependence of criticality on activation energy when reactant consumption is neglected
    Combustion and Flame, vol. 33, pp. 161–168, 1978
  93. Perturbations of the spectrum of nonlinear eigenvalue problems
    Journal of Mathematical Analysis and Applications, vol. 66, no. 2, pp. 433–441, 1978
  94. Criteria for Thermal Explosions with and without Reactant Consumption
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990), vol. 357, no. 1691, pp. 403–422, 1977
  95. Nonlinear eigenvalue problems with mixed boundary conditions
    Journal of Mathematical Analysis and Applications, vol. 48, no. 3, pp. 721–735, 1974
  96. Variational methods for nonlinear eigenvalue problems associated with thermal ignition
    Journal of Differential Equations, vol. 13, no. 2, pp. 247–256, 1973
  97. Estimation of critical parameters in thermal ignition
    Combustion and Flame, vol. 21, no. 1, pp. 119–121, 1973
  98. Uniqueness theorem for a system of parabolic differential equations
    Journal of Differential Equations, vol. 6, no. 1, pp. 36–39, 1969
  99. On comparison theorems for multicomponent diffusion systems
    Journal of Mathematical Analysis and Applications, vol. 26, no. 2, pp. 292–296, 1969