Applied Math

Duke Applied Mathematics



Publications of David G Schaeffer    :chronological  alphabetical  combined  bibtex listing:

Books

  1. Two phase flows and waves, edited by Joseph, Daniel D. and Schaeffer, David G., pp. xii+164, 1990, Springer-Verlag, New York [MR91e:76008]
  2. Golubitsky, Martin and Stewart, Ian and Schaeffer, David G., Singularities and groups in bifurcation theory. Vol. II, pp. xvi+533, 1988, Springer-Verlag, New York [MR89m:58038]
  3. Golubitsky, Martin and Schaeffer, David G., Singularities and groups in bifurcation theory. Vol. I, pp. xvii+463, 1985, Springer-Verlag, New York [MR86e:58014]

Papers Published

  1. S. Dai and D.G. Schaeffer, Bifurcation in a modulation equation for alternans in a cardiac fiber, ESAIM Mathematical modelling and numerical analysis, vol. 44 no. 6 (Winter, 2010)
  2. S. Dai and D.G. Schaeffer, Chaos in a one-dimensional model for cardiac dynamics, Chaos, vol. 20 no. 2 (June, 2010)
  3. D.G. Schaeffer and Shu Dai, Spectrum of a linearized amplitude equation for alternans in a cardiac fiber, SIAM Applied Math, vol. 69 no. 3 (December, 2008) [doi]
  4. D.G. Schaeffer, M. Beck, C. Jones, and M. Wechselberger, Electrical waves in a one-dimensional model of cardiac tissue, SIAM Applied Dynamical Systems, vol. 7 no. 4 (December, 2008) [doi]
  5. D.G. Schaeffer and R. Iverson, Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback, SIAM Applied Math, vol. 69 no. 3 (December, 2008) [doi]
  6. D.G. Schaeffer, J. Cain, Shortening of action potential duraction near an insulating boundary, Math Medicine and Biology, vol. 25 no. 21--36 (2008)
  7. D.G. Schaeffer, A. Catlla, T. Witelski, E. Monson, A. Lin, On spiking models of synaptic activity and impulsive differential equations, SIAM Review, vol. 50 no. 553--569 (2008)
  8. D.G. Schaeffer, W. Ying, X. Zhao, Asymptotic approximation of an ionic model for cardiac restitution, Nonlinear Dynamics, vol. 51 (2008), pp. 189--198
  9. D.G. Schaeffer, X. Zhao, Alternate pacing of border-collision period-doubling bifurcations, Nonlinear Dynamics, vol. 50 (2007), pp. 733--742
  10. D.G. Schaeffer, C. Berger, D. Gauthier, H. Dobrovolny, W. Krassowska, X. Zhao, Period-doubling bifurcation to alternans in paced cardiac tissue: crossover from smooth to border-collision characteristics, Phys. Rev. Lett, vol. 99 (2007), pp. 058101
  11. D.G. Schaeffer, C. Berger, D. Gauthier, X. Zhao, Small-signal amplification of period-doubling bifurcations in smooth iterated mappings, Nonlinear Dynamics, vol. 48 (2007), pp. 381--389
  12. D.G. Schaeffer, M Shearer, and T. Witelski, Boundary-value problems for hyperbolic partial differential equations related to steady granular flow, Math. and Mech. of Solids, vol. 12 (2007), pp. 665--699
  13. D.G. Schaeffer, J. Cain, D. Gauthier,S. Kalb, W. Krassowska, R. Oliver, E. Tolkacheva, W. Ying, An ionically based mapping model with memory for cardiac restitution, Bull Math Bio, vol. 69 (2007), pp. 459--482
  14. D.G. Schaeffer, M. Matthews, P. Gremaud, On the computation of steady hopper flows III: Comparison of von Mises and Matsuoka-Nakai materials", J Comp. Phy., vol. 219 (2006), pp. 443-454
  15. D.G. Schaeffer, S. Kalb, E. Tolkacheva, D. Gauthier, W. Krassowska, Features of the restitution portrait for mapping models with an arbitrary amount of memory, Chaos, vol. 15 (2005), pp. 023701--
  16. D.G. Schaeffer, B. Tighe, J. Socolar, G. Michener, M. Huber, Force distribution in granular media, PRE, vol. 72 (2005), pp. 031306
  17. D.G. Schaeffer, J. Cain, E. Tolkacheva, D. Gauthier, Rate-dependent waveback velocity of cardiac action potentials in a done-dimensional cable, Phys Rev E, vol. 70 (2004), pp. 061906--?
  18. David G. Schaeffer, J.V. Matthews, A steady-state, hyperbolic free boundary problem for a granular-flow model, SIAM J. Math Analysis, vol. 36 (2004), pp. 256-271
  19. David G. Schaeffer, M. Shearer, T. Witelski, One-dimensional solutions of an elastoplasticity model of granular material, Math. Models and Methods in Appl. Sciences, vol. 13 (2003), pp. 1629--1671
  20. Colleen C. Mitchell, David G. Schaeffer, A two-current model for the dynamics of cardiac membrane, Bulletin Math Bio, vol. 65 (2003), pp. 767--793
  21. David G. Schaeffer, E. Tolkacheva, D. Gauthier, W Krassowska, Condition for alternans and stability of the 1:1 response pattern in a 'memory' model of paced cardiac dynamics, Phys Rev E, vol. 67 (2003), pp. 031904
  22. David G. Schaeffer, Review of W. Cheney's "Analysis for applied mathematics", Amer. Math Monthly, vol. 110 (2003), pp. 550
  23. Pierre Gremaud, John V. Matthews, David G. Schaeffer, Secondary circulation in granular flow through a nonaxisymmetric hopper, SIAM J Appl. Math, vol. 64 (2003), pp. 583--600
  24. D.G. Schaeffer, E. Tolkacheva, D. Gauthier, W. Krassowska, Condition for alternans and stability of the 1:1 response pattern in a memory model of paced cardiac dynamics, Phys Rev E, vol. 67 (2003), pp. 031904
  25. David G. Schaeffer, Elena Tolkacheva, Colleen Mitchell, Analysis of the Fenton-Karma model through a one-dimensional map, Chaos, vol. 12 (2002), pp. 1034-1042
  26. David G. Schaeffer, J. Socolar, P. Claudin, J.-P. Bouchard, Directed force chain models and stress reponse in static granular materials, Euro. Phys. J. E, vol. 7 (2002), pp. 353--370
  27. D.G. Schaeffer, E. Tolkacheva, D. Gauthier, and C. Mitchell, Analysis of the Fenton-Karma model through approximation by a one-dimensional map, Chaos, vol. 12 (2002), pp. 1034
  28. Witelski, Thomas P. and Schaeffer, David G. and Shearer, Michael, A discrete model for an ill-posed nonlinear parabolic PDE, Phys. D, vol. 160, no. 3-4, pp. 189--221, 2001 [MR1872040]
  29. G. Metcalfe, L. Kondic, D. Schaeffer, S. Tennakoon, and R. Behringer, Granular friction and the fluid-solid transition for shaken granular materials, Phys. Rev. E 65 (2002)
  30. Hayes, Brian T. and Schaeffer, David G., Stress-controlled shear waves in a saturated granular medium, European J. Appl. Math., vol. 11, no. 1, pp. 81--94, 2000 [MR2000k:74037]
  31. David G Schaeffer, M. Sexton, J. Socolar, Force Distribution in a Scalar Model for Non-Cohesive Granular Material, Phys. Rev. Lett. E 60 (1999), 1999-2008
  32. Gremaud, Pierre Alain and Schaeffer, David G. and Shearer, Michael, Numerical determination of flow corrective inserts for granular materials in conical hoppers, Internat. J. Non-Linear Mech., vol. 35, no. 5, pp. 869--882, 2000 [MR2001a:76129]
  33. Hayes, Brian T. and Schaeffer, David G., Plane shear waves under a periodic boundary disturbance in a saturated granular medium, Phys. D, vol. 121, no. 1-2, pp. 193--212, 1998 [MR99g:73052]
  34. Howle, Laurens and Schaeffer, David G. and Shearer, Michael and Zhong, Pei, Lithotripsy: the treatment of kidney stones with shock waves, SIAM Rev., vol. 40, no. 2, pp. 356--371 (electronic), 1998 [MR99d:92009]
  35. David G Schaeffer, M. Shearer, A Simple Model for Stress Fluctuations in Plasticity, with Application to Granular Materials, SIAM J. Appl. Math. 58(1998), 1791-1807.
  36. G. Tardos, M.I. Khan, David G Schaeffer, Forces On a Slowly Rotating, Rough Cylinder in a Couette Device Containing a Dry, Frictional Powder, Physics of Fluids 10(1998), 335-341.
  37. Schaeffer, David G. and Shearer, Michael, The influence of material non-uniformity preceding shear-band formation in a model for granular flow, European J. Appl. Math., vol. 8, no. 5, pp. 457--483, 1997 [MR98g:73016]
  38. M. K. Gordon, David G Schaeffer, M. Shearer, Plane Shear Waves in a Fully Saturated Granular Medium with Velocity-and Stress-Controlled Boundary Conditions, Int. J. Nonlinear Mechancis 32(1997), 489-503.
  39. P. Gremaud, David G Schaeffer, Ml. Shearer, Granular Flow Past a Binsert, Report to Jenike & Johanson, Inc.
  40. David G Schaeffer, M. Shearer, Models of Stress Fluctuations in Granular Materials, Powders and Grains, R.P. Behringer and J. Jenkins (eds.), Balkema, 1997.
  41. Shearer, Michael and Schaeffer, David G., Riemann problems for $5\times 5$ systems of fully non-linear equations related to hypoplasticity, Math. Methods Appl. Sci., vol. 19, no. 18, pp. 1433--1444, 1996 [MR97m:73028]
  42. Schaeffer, David G., A survey of granular flow, Hyperbolic problems: theory, numerics, applications (Stony Brook, NY, 1994), pp. 63--80, 1996, World Sci. Publishing, River Edge, NJ [MR1446015]
  43. David G Schaeffer, Memoirs From a Small-Scale Course On Industrial Math, Notices AMS, 43(1996), 550-557.
  44. Shearer, Michael and Schaeffer, David G., A class of fully nonlinear $2\times 2$ systems of partial differential equations, Comm. Partial Differential Equations, vol. 20, no. 7-8, pp. 1105--1131, 1995 [MR96b:35133]
  45. Shearer, Michael and Schaeffer, David G., Fully nonlinear hyperbolic systems of partial differential equations related to plasticity, Comm. Partial Differential Equations, vol. 20, no. 7-8, pp. 1133--1153, 1995 [MR96b:35134]
  46. Garaizar, F. Xabier and Schaeffer, David G., Numerical computations for shear bands in an antiplane shear model, J. Mech. Phys. Solids, vol. 42, no. 1, pp. 21--50, 1994 [MR94j:73029]
  47. Gardner, Carl L. and Schaeffer, David G., Numerical simulation of uniaxial compression of a granular material with wall friction, SIAM J. Appl. Math., vol. 54, no. 6, pp. 1676--1692, 1994 [MR95g:76010]
  48. Shearer, Michael and Schaeffer, David G., Unloading near a shear band in granular material, Quart. Appl. Math., vol. 52, no. 3, pp. 579--600, 1994 [MR95m:73030]
  49. F.X. Garzizar, David G Schaeffer, M. Shearer, J. Trangenstein, Formation and Development of Shear Bands in Granular Material, Trans. of 11th Army Conf. on Appl. Math. & Computing.
  50. Shearer, Michael and Schaeffer, David G., The initial value problem for a system modelling unidirectional longitudinal elastic-plastic waves, SIAM J. Math. Anal., vol. 24, no. 5, pp. 1111--1144, 1993 [MR95f:73038]
  51. Schaeffer, David G. and Shearer, Michael, Unloading near a shear band: a free boundary problem for the wave equation, Comm. Partial Differential Equations, vol. 18, no. 7-8, pp. 1271--1298, 1993 [MR94i:35203]
  52. Schaeffer, David G. and Schecter, Stephen and Shearer, Michael, Non-strictly hyperbolic conservation laws with a parabolic line, J. Differential Equations, vol. 103, no. 1, pp. 94--126, 1993 [MR94d:35102]
  53. Schaeffer, David G., A mathematical model for localization in granular flow, Proc. Roy. Soc. London Ser. A, vol. 436, no. 1897, pp. 217--250, 1992 [MR93g:73061]
  54. Schaeffer, David G. and Shearer, Michael, Scale-invariant initial value problems in one-dimensional dynamic elastoplasticity, with consequences for multidimensional nonassociative plasticity, European J. Appl. Math., vol. 3, no. 3, pp. 225--254, 1992 [MR93g:73057]
  55. An, Lian Jun and Schaeffer, David G., The flutter instability in granular flow, J. Mech. Phys. Solids, vol. 40, no. 3, pp. 683--698, 1992 [MR93c:73053]
  56. Wang, Feng and Gardner, Carl L. and Schaeffer, David G., Steady-state computations of granular flow in an axisymmetric hopper, SIAM J. Appl. Math., vol. 52, no. 4, pp. 1076--1088, 1992 [MR93c:73040]
  57. Schaeffer, David G. and Shearer, Michael, Loss of hyperbolicity in yield vertex plasticity models under nonproportional loading, Nonlinear evolution equations that change type, pp. 192--217, 1990, Springer, New York [MR92f:73022]
  58. Schaeffer, David G., Mathematical issues in the continuum formulation of slow granular flow, Two phase flows and waves (Minneapolis, MN, 1989), pp. 118--129, 1990, Springer, New York [MR91f:73014]
  59. Schaeffer, David G., Instability and ill-posedness in the deformation of granular materials, Internat. J. Numer. Anal. Methods Geomech., vol. 14, no. 4, pp. 253--278, 1990 [MR91e:73071]
  60. Schaeffer, David G. and Shearer, Michael and Pitman, E. Bruce, Instability in critical state theories of granular flow, SIAM J. Appl. Math., vol. 50, no. 1, pp. 33--47, 1990 [MR90k:73044]
  61. Shearer, Michael and Schaeffer, David G., The quasidynamic approximation in critical state plasticity, Arch. Rational Mech. Anal., vol. 108, no. 3, pp. 267--280, 1989 [MR91d:73031]
  62. Pitman, E. Bruce and Schaeffer, David G., Instability and ill-posedness in granular flow, Current progress in hyberbolic systems: Riemann problems and computations (Brunswick, ME, 1988), pp. 241--250, 1989, Amer. Math. Soc., Providence, RI [MR90k:73037]
  63. Schaeffer, David G. and Pitman, E. Bruce, Ill-posedness in three-dimensional plastic flow, Comm. Pure Appl. Math., vol. 41, no. 7, pp. 879--890, 1988 [MR89m:73018]
  64. Beale, J. Thomas and Schaeffer, David G., Nonlinear behavior of model equations which are linearly ill-posed, Comm. Partial Differential Equations, vol. 13, no. 4, pp. 423--467, 1988 [MR89h:35329]
  65. Schaeffer, David G. and Shearer, Michael, Riemann problems for nonstrictly hyperbolic $2\times 2$ systems of conservation laws, Trans. Amer. Math. Soc., vol. 304, no. 1, pp. 267--306, 1987 [MR88m:35101]
  66. Pitman, E. Bruce and Schaeffer, David G., Stability of time dependent compressible granular flow in two dimensions, Comm. Pure Appl. Math., vol. 40, no. 4, pp. 421--447, 1987 [MR88i:35170]
  67. Schaeffer, David G., Instability in the evolution equations describing incompressible granular flow, J. Differential Equations, vol. 66, no. 1, pp. 19--50, 1987 [MR88i:35169]
  68. Shearer, M. and Schaeffer, D. G. and Marchesin, D. and Paes-Leme, P. L., Solution of the Riemann problem for a prototype $2\times 2$ system of nonstrictly hyperbolic conservation laws, Arch. Rational Mech. Anal., vol. 97, no. 4, pp. 299--320, 1987 [MR88a:35156]
  69. Schaeffer, David G. and Shearer, Michael, The classification of $2\times 2$ systems of nonstrictly hyperbolic conservation laws, with application to oil recovery, Comm. Pure Appl. Math., vol. 40, no. 2, pp. 141--178, 1987 [MR88a:35155]
  70. Shearer, Michael and Schaeffer, David G., Recent developments in nonstrictly hyperbolic conservation laws, Transactions of the fourth Army conference on applied mathematics and computing (Ithaca, N.Y., 1986), pp. 43--52, 1987, U.S. Army Res. Office, Research Triangle Park, NC [MR905075]
  71. Schaeffer, David G. and Shearer, Michael, Three phase flow in a porous medium and the classification of nonstrictly hyperbolic conservation laws, International workshop on applied differential equations (Beijing, 1985), pp. 154--162, 1986, World Sci. Publishing, Singapore [MR89c:35100]
  72. Shearer, Michael and Schaeffer, David G., Three-phase flow in a porous medium and the classification of non-strictly hyperbolic conservation laws, Transactions of the third Army conference on applied mathematics and computing (Atlanta, Ga., 1985), pp. 509--517, 1986, U.S. Army Res. Office, Research Triangle Park, NC [MR87j:76093]
  73. Schaeffer, David G., Instability in the flow of granular materials, Mathematics applied to fluid mechanics and stability (Troy, N.Y., 1985), pp. 274, 1986, SIAM, Philadelphia, PA [MR869642]
  74. Golubitsky, M. and Marsden, J. and Schaeffer, D., Bifurcation problems with hidden symmetries, Partial differential equations and dynamical systems, pp. 181--210, 1984, Pitman, Boston, MA [MR86a:58020]
  75. Holder, E. J. and Schaeffer, D., Boundary conditions and mode jumping in the von K\'arm\'an equations, SIAM J. Math. Anal., vol. 15, no. 3, pp. 446--458, 1984 [MR85m:73029]
  76. Schaeffer, David G., Topics in bifurcation theory, Systems of nonlinear partial differential equations (Oxford, 1982), pp. 219--262, 1983, Reidel, Dordrecht [MR85e:58107]
  77. Golubitsky, Martin and Schaeffer, David, A discussion of symmetry and symmetry breaking, Singularities, Part 1 (Arcata, Calif., 1981), pp. 499--515, 1983, Amer. Math. Soc., Providence, RI [MR85b:58018]
  78. Ball, J. M. and Schaeffer, D. G., Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions, Math. Proc. Cambridge Philos. Soc., vol. 94, no. 2, pp. 315--339, 1983 [MR84k:73033]
  79. Golubitsky, Martin and Schaeffer, David, Bifurcations with ${\rm O}(3)$\ symmetry including applications to the B\'enard problem, Comm. Pure Appl. Math., vol. 35, no. 1, pp. 81--111, 1982 [MR83b:58026]
  80. Schaeffer, David, General introduction to steady state bifurcation, Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), pp. 13--47, 1981, Springer, Berlin [MR83j:58037]
  81. Golubitsky, Martin and Keyfitz, Barbara Lee and Schaeffer, David G., A singularity theory analysis of a thermal-chainbranching model for the explosion peninsula, Comm. Pure Appl. Math., vol. 34, no. 4, pp. 433--463, 1981 [MR82h:58010]
  82. Schaeffer, David G. and Golubitsky, Martin A., Bifurcation analysis near a double eigenvalue of a model chemical reaction, Arch. Rational Mech. Anal., vol. 75, no. 4, pp. 315--347, 1980/81 [MR83b:80010]
  83. Golubitsky, Martin and Keyfitz, Barbara L. and Schaeffer, David, A singularity theory approach to qualitative behavior of complex chemical systems, New approaches to nonlinear problems in dynamics (Proc. Conf., Pacific Grove, Calif., 1979), pp. 257--270, 1980, SIAM, Philadelphia, Pa. [MR82i:80011]
  84. Golubitsky, Martin and Schaeffer, David, A singularity theory approach to steady-state bifurcation theory, Nonlinear partial differential equations in engineering and applied science (Proc. Conf., Univ. Rhode Island, Kingston, R.I., 1979), pp. 229--254, 1980, Dekker, New York [MR82a:58018]
  85. Golubitsky, Martin and Schaeffer, David, A qualitative approach to steady-state bifurcation theory, New approaches to nonlinear problems in dynamics (Proc. Conf., Pacific Grove, Calif., 1979), pp. 43--51, 1980, SIAM, Philadelphia, Pa. [MR81k:58026]
  86. Schaeffer, David G., Qualitative analysis of a model for boundary effects in the Taylor problem, Math. Proc. Cambridge Philos. Soc., vol. 87, no. 2, pp. 307--337, 1980 [MR81c:35007]
  87. Schaeffer, David and Golubitsky, Martin, Boundary conditions and mode jumping in the buckling of a rectangular plate, Comm. Math. Phys., vol. 69, no. 3, pp. 209--236, 1979 [MR81k:35019]
  88. Golubitsky, M. and Schaeffer, D., An analysis of imperfect bifurcation, Bifurcation theory and applications in scientific disciplines (Papers, Conf., New York, 1977), pp. 127--133, 1979, New York Acad. Sci., New York [MR81c:58027]
  89. Golubitsky, M. and Schaeffer, D., A theory for imperfect bifurcation via singularity theory, Comm. Pure Appl. Math., vol. 32, no. 1, pp. 21--98, 1979 [MR80j:58061]
  90. Golubitsky, M. and Schaeffer, D., Imperfect bifurcation in the presence of symmetry, Comm. Math. Phys., vol. 67, no. 3, pp. 205--232, 1979 [MR80j:58017]
  91. Schaeffer, David G., An application of the Nash-Moser theorem to a free boundary problem, Nonlinear partial differential equations and applications (Proc. Special Sem., Indiana Univ., Bloomington, Ind., 1976-1977), pp. 129--143, 1978, Springer, Berlin [MR80c:35067]
  92. Schaeffer, David G., Non-uniqueness in the equilibrium shape of a confined plasma, Comm. Partial Differential Equations, vol. 2, no. 6, pp. 587--600, 1977 [MR58:29210]
  93. Schaeffer, David G., Some examples of singularities in a free boundary, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), vol. 4, no. 1, pp. 133--144, 1977 [MR58:24345]
  94. Schaeffer, David G., One-sided estimates for the curvature of the free boundary in the obstacle problem, Advances in Math., vol. 24, no. 1, pp. 78--98, 1977 [MR56:6506]
  95. Guillemin, Victor and Schaeffer, David, On a certain class of Fuchsian partial differential equations, Duke Math. J., vol. 44, no. 1, pp. 157--199, 1977 [MR55:3504]
  96. Schaeffer, David G., Supersonic flow past a nearly straight wedge, Duke Math. J., vol. 43, no. 3, pp. 637--670, 1976 [MR54:1850]
  97. Schaeffer, David G., A new proof of the infinite differentiability of the free boundary in the Stefan problem, J. Differential Equations, vol. 20, no. 1, pp. 266--269, 1976 [MR52:11325]
  98. Schaeffer, David G., Singularities and the obstacle problem, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 2, pp. 339--340, 1975, Amer. Math. Soc., Providence, R.I. [MR57:10227]
  99. Schaeffer, David G., On the existence of discrete frequencies of oscillation in a rotating fluid, Studies in Appl. Math., vol. 54, no. 3, pp. 269--274, 1975 [MR56:10385]
  100. Schaeffer, David G., An example of generic regularity for a non-linear elliptic equation, Arch. Rational Mech. Anal., vol. 57, pp. 134--141, 1975 [MR52:8649]
  101. Guillemin, V. and Schaeffer, D., Fourier integral operators from the Radon transform point of view, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 2, pp. 297--300, 1975, Amer. Math. Soc., Providence, R.I. [MR52:1420]
  102. Schaeffer, David G., A stability theorem for the obstacle problem, Advances in Math., vol. 17, no. 1, pp. 34--47, 1975 [MR52:994]
  103. Golubitsky, Martin and Schaeffer, David G., Stability of shock waves for a single conservation law, Advances in Math., vol. 16, pp. 65--71, 1975 [MR51:10889]
  104. Schaeffer, David G., The capacitor problem, Indiana Univ. Math. J., vol. 24, no. 12, pp. 1143--1167, 1974/75 [MR52:14607]
  105. Guillemin, V. and Schaeffer, D., Remarks on a paper of D. Ludwig, Bull. Amer. Math. Soc., vol. 79, pp. 382--385, 1973 [MR53:13800]
  106. Schaeffer, David G., An application of von Neumann algebras to finite difference equations, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971), pp. 183--194, 1973, Amer. Math. Soc., Providence, R.I. [MR49:838]
  107. Schaeffer, David G., A regularity theorem for conservation laws, Advances in Math., vol. 11, pp. 368--386, 1973 [MR48:4523]
  108. Schaeffer, David G., An index theorem for systems of difference operators on a half space, Inst. Hautes \'Etudes Sci. Publ. Math., no. 42, pp. 121--127, 1973 [MR47:9341]
  109. Schaeffer, David G., Approximation of the Dirichlet problem on a half space, Acta Math., vol. 129, no. 3--4, pp. 281--295, 1972 [MR52:16058]
  110. Schaeffer, David G., An application of von Neumann algebras to finite difference equations, Ann. of Math. (2), vol. 95, pp. 117--129, 1972 [MR45:5563]
  111. Coburn, L. A. and Douglas, R. G. and Schaeffer, D. G. and Singer, I. M., $C\sp{\ast} $-algebras of operators on a half-space. II. Index theory, Inst. Hautes \'Etudes Sci. Publ. Math., no. 40, pp. 69--79, 1971 [MR50:10884]
  112. Schaeffer, David G., Wiener-Hopf factorization of the symbol of an elliptic difference operator, J. Functional Analysis, vol. 5, pp. 383--394, 1970 [MR41:7491]
  113. Schaeffer, David G., An extension of Hartogs' theorem for domains whose boundary is not smooth, Proc. Amer. Math. Soc., vol. 25, pp. 714--715, 1970 [MR41:5650]
  114. Schaeffer, David G., The Dirichlet problem with generalized functions as data, Ann. Mat. Pura Appl. (4), vol. 83, pp. 153--174, 1969 [MR41:7271]
  115. Schaeffer, David G., A note on the representation of a solution of an elliptic differential equation near an isolated singularity, Proc. amer. Math. Soc., vol. 23, pp. 450--454, 1969 [MR39:7262]

Papers Submitted

  1. K. Gonzales, Omur Kayikci, D.G. Schaeffer, and P. Magwene, Modeling mutant phenotypes and oscillatory dynamics in the \emph{Saccharomyces cerevisiae} cAMP-PKA pathway, PLoS Computational Biology (Winter, 2010)
  2. S. Payne, B. Li, H. Song, D.G. Schaeffer, and L. You, Self-organized pattern formation by a pseudo-Turing mechanism (Winter, 2010)
  3. Y. Farjoun, D.G. Schaeffer, The hanging thin rod: a singularly perturbed eigenvalue problem, SIAM Sppl. Math. (July, 2010)

Preprints

  1. D.G. Schaeffer, A. Catlla, T. Witelski, E. Monson, A. Lin, Annular patterns in reaction-diffusion systems and their implications for neural-glial interactions (2008)

Duke University * Arts & Sciences * Mathematics * August 23, 2014

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