Research

Main research interests:

  • Partial Differential Equations
  • Applied Mathematics
  • Mathematical Biology
Refereed research journal publications:
  1. On the blowup of ut at quenching (with H. A. Levine), Proc. Amer. Math. Soc. 106 (1989), 1049-1056.
  2. Quenching for solutions of a plasma type equation, Nonlinear Anal. TMA 18 (1992), 731-742.
  3. The influence of nonlocal nonlinearities on the long time behavior of solutions of Burgers's equation (with M. K. Kwong and H. A. Levine), Quart. Appl. Math. 50 (1992), 173-200.
  4. Comparison principle for some nonlocal problems, Quart. Appl. Math. 50 (1992), 517-522.
  5. Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179 (1993), 630-637.
  6. On the existence and nonexistence of global solutions of a diffusion-advection equation, Proc. Royal Soc. Edinburgh Sect. A 123 (1993), 1099-1108.
  7. Stabilization of solutions of a nonlinear parabolic equation with a gradient term, Math. Zeitschrift 216 (1994), 147-155.
  8. Behavior of solutions of Burgers' equation with nonlocal boundary conditions, J. Differential Equations 113 (1994), 394-417.
  9. Behavior of solutions of Burgers' equation with nonlocal boundary conditions (II), Quart. Appl. Math. 52 (1994), 553-567.
  10. The blow-up behavior of the heat equation with Neumann boundary conditions, J. Math. Anal. Appl. 188 (1994), 641-650.
  11. On critical exponents for a system of heat equations coupled in the boundary conditions (with M. Fila and H. A. Levine), Acta. Math. Univ. Comenianae 63 (1994), 169-192.
  12. Dynamical behavior of solutions of a semilinear heat equation with nonlocal singularity, SIAM J. Math. Anal. 26 (1995), 98-111.
  13. Global existence and blow-up for a system of heat equations with non-linear boundary conditions, Math. Methods Appl. Sci. 18 (1995), 307-315.
  14. Global existence for nonlinear diffusion equations (with J. R. Anderson), J. Math. Anal. Appl. 196 (1995), 479-501.
  15. Nonlocal nonlinearity versus global blow-up, Mathematica Applicata 8 (1995), 124-129.
  16. Coupled Volterra equations with blow-up solutions (with W. E. Olmstead and C. A. Roberts), J. Integral Equations Appl. 7 (1995), 499-516.
  17. Impulsive effects on global existence of solutions of semilinear heat equations (with C. Y. Chan), Nonlinear Anal. TMA 26 (1996), 1481-1489.
  18. Blow-up rates for parabolic systems, Z. Angew. Math. Phys. 47 (1996), 132-143.
  19. Nonexistence of entire solutions of a coupled elliptic system, Funkcialaj Ekvacioj 39 (1996), 541-551.
  20. Quenching for a diffusive equation with a concentrated singularity (with C. A. Roberts), Differential Integral Equations 10 (1997), 369-379.
  21. Nonexistence of global solutions of a nonlinear hyperbolic system, Trans. Amer. Math. Soc. 349 (1997), 1685-1696.
  22. Global existence for degenerate parabolic equations with a non-local forcing (with J. R. Anderson), Math. Methods Appl. Sci. 20 (1997), 1069-1087.
  23. Monotone method for first order nonlocal hyperbolic initial-boundary value problems (with A. S. Ackleh), Appl. Anal. 67 (1997), 283-293.
  24. Behavior of solutions of a nonlinear ordinary differential equation (with M. Xu), J. Math. Anal. Appl. 218 (1998), 269-282.
  25. Remarks on blow-up behavior for a nonlinear diffusion with Neumann boundary conditions (with M. Xu), Proc. Amer. Math. Soc. 127 (1999), 167-172.
  26. A monotone approximation for the nonautonomous size-structured population model (with A. S. Ackleh), Quart. Appl. Math. 57 (1999), 261-267.
  27. Quenching for a nonlinear diffusion equation with a singular boundary condition (with M. Xu), Z. Angew. Math. Phys. 50 (1999), 574-584.
  28. Blow-up of solutions of some nonlinear hyperbolic systems, Rocky Mountain J. Math. 29 (1999), 807-820.
  29. A monotone approximation for a nonlinear nonautonomous size-structured population model (with A. S. Ackleh), Appl. Math. Comp. 108 (2000), 103-113.
  30. On solutions of a singular diffusion equation (with M. Xu), Nonlinear Anal. TMA 41 (2000), 489-500.
  31. Monotone scheme for nonlinear first order hyperbolic initial-boundary value problems (with A. S. Ackleh), Appl. Math. Letters 13 (2000), 111-119.
  32. The role of critical exponents in blow-up theorems: the sequel (with H. A. Levine), J. Math. Anal. Appl. 243 (2000), 85-126.
  33. Quenching versus blow-up (with C.-L. Zhao), J. Partial Differential Equations 13 (2000), 243-252.
  34. Existence-uniqueness of solutions for a nonlinear nonautonomous size-structured population model: an upper-lower solution approach (with A. S. Ackleh), Canadian Appl. Math. Quart. 8 (2000), 1-15.
  35. Existence and nonexistence of global solutions of the wave equation with a nonlinear boundary condition (with A. S. Ackleh), Quart. Appl. Math. 59 (2001), 153-158.
  36. Global existence and blow-up for a system of wave equations coupled in the boundary conditions (with A. S. Ackleh), Dynamics Contin. Discrete Impuls. Systems Ser. A 8 (2001), 415-424.
  37. Blow-up for a parabolic system coupled in an equation and a boundary condition (with C.-L. Zhao), Proc. Royal Soc. Edinburgh Sect. A 131 (2001), 1345-1355.
  38. Positive solutions of a nonlinear ordinary differential equation (with C.-L. Zhao), Differential Integral Equations 15 (2002), 607-622.
  39. A finite difference approximation for a coupled system of nonlinear size-structured populations (with A. S. Ackleh and H. T. Banks), Nonlinear Anal. TMA 50 (2002), 727-748.
  40. Numerical investigation of quenching for a nonlinear diffusion equation with a singular Neumann boundary condition (with C. I. Christov), Numer. Methods Partial Differential Eqauations 18 (2002), 429-440.
  41. Blow-up versus quenching (with C.-L. Zhao), Comm. Appl. Anal. 7 (2003), 87-100.
  42. Solvability of a nonlocal hyperbolic model arising from a reliability system (with A. S. Ackleh and W. Li), IMA J. Appl. Math. 68 (2003), 135-148.
  43. On a first order hyperbolic coagulation model (with A. S. Ackleh), Math. Methods Appl. Sci. 26 (2003), 703-715.
  44. Existence-uniqueness results for a system of integral equations arising from a reliability model (with A. S. Ackleh), Comm. Appl. Nonlinear Anal. 10 (2003), 23-32.
  45. A numerical method for a nonlocal hyperbolic model arising from a reliability system (with A. S. Ackleh, J. Derouen, and W. Li), Comp. Math. Appl. 47 (2004), 135-147.
  46. Existence-uniqueness and monotone approximation for an erythropoiesis age-structured model (with A. S. Ackleh, C. Cole, and H. Tran), J. Math. Anal. Appl. 289 (2004), 530-544.
  47. Existence and nonexistence of global solutions of a nonlocal wave equation (with A. S. Ackleh), Math. Methods Appl. Sci. 27 (2004), 1747-1754.
  48. Survival of the fittest in a quasilinear size-structured population model (with A. S. Ackleh), Natural Resource Modeling 17 (2004), 213-228.
  49. On critical exponent for the Schrodinger equation with a nonlinear boundary condition (with A. S. Ackleh), Differential Integral Equations 17 (2004), 1293-1307.
  50. Competitive exclusion and coexistence in a quasilinear size-structured population model (with A. S. Ackleh and X. Wang), Math. Biosci. 192 (2004), 177-192.
  51. A quasilinear hierarchical size structured model: well-posedness and approximation (with A. S. Ackleh and S. Hu), Appl. Math. Optim. 51 (2005), 35-59.
  52. Instability of solutions of a semilinear heat equation with a Neumann boundary condition (with C.-L. Zhao), Quart. Appl. Math. 63 (2005), 13-19.
  53. Monotone approximation for a hierarchical age-structured population model (with A. S. Ackleh), Dynamics Contin. Discrete Impuls. Systems Ser. B 12 (2005), 203-214.
  54. Parameter estimation in a coupled system of nonlinear size-structured populations (with A. S. Ackleh, H. T. Banks, and S. Hu), Math. Biosci. Engineering 2 (2005), 289-315.
  55. Global existence and blow-up for a system of nonlocal wave equations, Mathematica Applicata 18 (2005), 181-187.
  56. Existence-uniqueness and monotone approximation for a phytoplankton-zooplankton aggregation model (with A. S. Ackleh and X. Wang), Z. Angew. Math. Phys. 57 (2006), 733-749.
  57. A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate (with A. S. Ackleh, K. Ito, and J. Thibodeaux), Math. Biosci. 204 (2006), 21-48.
  58. Asymptotic behavior of solutions to a nonlinear size-structured population model (with A. S. Ackleh and X. Wang), Internat. J. Info. Systems Sci. 2 (2006), 316-325.
  59. On a nonlinear size-structured phytoplankton-zooplankton aggregation model (with A. S. Ackleh and S. Hu), Dynamics Contin. Discrete Impuls. Systems Ser. A 14 (2007), 265-285.
  60. A monotone approximation for a size-structured population model with a generalized environment ( (with A. S. Ackleh and J. Thibodeaux), J. Biol. Dynamics 1 (2007), 305-319.
  61. On a nonlocal reaction-diffusion population model, Discrete Contin. Dynam. Systems Ser. B. 9 (2008), 65-73.
  62. A nonautonomous juvenile-adult model: well-posedness and long-time behavior via a comparison principle (with A. S. Ackleh), SIAM J. Appl. Math. 69 (2009), 1644-1661.
  63. Asymptotic behavior for a cellular replication and maturation model, J. Math. Anal. Appl. 360 (2009), 727-736.
  64. Stability of a delay equation arising from a juvenile-adult model (with A. S. Ackleh), Math. Biosci. Engineering 7 (2010), 729-737.
  65. Characteristic line based schemes for solving a quasilinear hierarchical size-structured model (with T. T. Marinov), J. Sci. Comput. 46 (2011), 452-469.
  66. Stochastic juvenile-adult models with application to a green tree frog population (with A. S. Ackleh and Q. Huang), J. Biol. Dynamics 5 (2011), 64-83.
  67. Global solvability for the heat equation with boundary flux governed by nonlinear memory (with J. R. Anderson and Z. Dong), Quart. Appl. Math. 69 (2011), 759-770.
  68. Fitting a structured juvenile–adult model for green tree frogs to population estimates from capture–mark–recapture field data (with A. S. Ackleh, J. Carter, Q. Huang, N. Pal, and X. Yang), Bull. Math. Biol. 74 (2012), 641-665.
  69. Sensitivity analysis for a structured juvenile-adult model (with A. S. Ackleh and X. Yang), Comp. Math. Appl. 64 (2012), 190-200.
  70. Blow-up for the heat equation with a general memory boundary condition (with Z. Dong), Comm. Pure Appl. Anal. 11 (2012), 2147-2156.
  71. Blow-up for a parabolic system with nonlinear memory (with Z. Dong), Dynamics Contin. Discrete Impuls. Systems Ser. A 19 (2012), 729-743.
  72. Blow-up rate for the heat equation with a memory boundary condition (with Q. Wang), Appl. Anal. 94 (2015), 308-317.
  73. Asymptotic behavior for a reaction-diffusion population model with delay (with Y. Wu), Discrete Contin. Dynam. Sys. Ser. B. 20 (2015), 385-395.
  74. A second order characteristic line scheme for solving a juvenile-adult model of amphibians (with Y. Wang), J. Biol. Dynamics 9 (2015), 51-63.
  75. Global solvability for the porous medium equation with boundary flux governed by nonlinear memory (with J. R. Anderson), J. Math. Anal. Appl. 423 (2015), 1183-1202.
  76. Analysis of a characteristics scheme for a quasilinear hierarchical size-structured model (with Y. Wang), Numer. Funct. Anal. Optim. 36 (2015), 329-349.
  77. Global stability for a nonlocal reaction-diffusion population model (with Y. Wu), Nonlinear Anal. Real World Appl. 25 (2015), 127-136.
  78. Sensitivity analysis for a nonlinear size-structured population model (with Y. Wang), Quart. Appl. Math. 73 (2015), 401-417.
  79. On the diffusive Nicholson's blowflies equation with distributed delay (with Y. Wu), Appl. Math. Letters 50 (2015), 126-132.
  80. Competitive exclusion and coexistence in a two-strain pathogen model with diffusion (with A. S. Ackleh and Y. Wu), Math. Biosci. Engineering 13 (2016), 1-18.
  81. Global existence and blow-up for the fast diffusion equation with a memory boundary condition (with Q. Wang), Quart. Appl. Math. 74 (2016), 189-199.
  82. Global behavior of solutions to the fast diffusion equation with boundary flux governed by memory (with J. R. Anderson and Q. Wang), Math. Methods Appl. Sci. 39 (2016), 4451-4462.
  83. Dynamics of a susceptible–infected–susceptible epidemic reaction–diffusion model (with Y. Wu), Proc. Royal Soc. Edinburgh Sect. A 146 (2016), 929-946.
  84. Extinction and uniform strong persistence of a size-structured population model (with Y. Wu), Discrete Contin. Dynam. Sys. Ser. B. 22 (2017), 831-840.
  85. A lower bound on the blow up time for solutions of a chemotaxis system with nonlinear chemotactic sensitivity (with J. R. Anderson), Nonlinear Anal. 159 (2017), 2-9.
  86. Asymptotic behavior of an SIR reaction-diffusion model with a linear source, Discrete Contin. Dynam. Sys. Ser. B. 24 (2019), 5945-5957.
  87. A hybrid parabolic and hyperbolic equation model for a population with separate dispersal and stationary stages: well-posedness and population persistence (with Q. Huang), SIAM J. Appl. Math. 79 (2019), 2265-2287.
  88. Global solvability for a diffusion model with absorption and memory-driven flux at the boundary (with J. R. Anderson), Z. Angew. Math. Phys. 71:50 (2020), 1-15.
  89. Analysis of age and spatially dependent population model: application to forest growth (with G. F. Webb and Y. Wu), Nonlinear Anal. Real World Appl. 56 (2020), 103164.
  90. Global attractivity of delayed and nonlocal diffusive logistic models with variable coefficients (with Y. Wu), J. Differential Equations, 299 (2021), 229-255.
  91. On a nonlinear nonlocal model for a population with separate dispersal and sedentary stages (with Q. Huang), Nonlinear Anal. Real World Appl. 62 (2021), 103366.
  92. Blow up and global solvability for an absorptive porous medium equation with memory at the boundary (with J. R. Anderson), IMA J. Appl. Math. 86 (2021), 1327-1348.
Refereed conference proceedings publications:
  1. Asymptotic behavior for a nonlinear nonautonomous size-structured population model (with A. S. Ackleh), Proc. 14th annual CAM, Edmond, Oklahoma, (1998), 8-12.
  2. Monotone method for nonlinear nonlocal hyperbolic problems (with A. S. Ackleh), E. J. Differential Equations Conf. 10 (2003), 11-22.
  3. An adaptive numerical method for the wave equation with a nonlinear boundary condition (with A. S. Ackleh and J. Derouen), E. J. Differential Equations Conf. 10 (2003), 23-31.
  4. On a nonlocal hyperbolic model arising from a reliability system (with A. S. Ackleh), Proc. Dynamic Systems Appl. 4 (2004), 113-120.
  5. An explicit finite difference method for a structured erythropoiesis model (with A. S. Ackleh and J. Thibodeaux), Proc. Dynamic Systems Appl. 5 (2008), 1-5.
  6. Characteristic line scheme for hierarchical size-structured model  with nonlinear growth, mortality and reproduction rates (with T. T. Marinov), 1st Internat. Conf. Appl. Math. Tech. Natural Sci. 1186 (2009), 123-132.
  7. Existence-uniqueness results and difference approximations for an amphibian juvenile-adult model (with A. S. Ackleh and Q. Huang), AMS Contemporary Math. 513 (2010), 1-23.
  8. Difference approximation for an amphibian juvenile-adult dispersal model (with A. S. Ackleh and Q. Huang), Dynamical Systems Differential Equations, DCDS Supp., Proc. 8th AIMS Internat. Conf. (2011), 1-12.