Research

Main research interests:

  • Partial Differential Equations
  • Mathematical Biology
  • Applied Mathematics
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. App. 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. 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.
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.