Dr. Shangbing Ai

Associate Professor, Mathematical Sciences Department

Education

  • Ph.D., University of Pittsburgh, 1999

Classes Taught


Publications

  • S. Ai, Yihong Du and Peng Rui, Traveling wave solutions for a Holling-Tanner predator-prey model, J. Diff. Eqns. to appear (published online Aug. 2017 [http://dx.doi.org/10.1016/j.jde.2017.08.021]).
  • S. Ai and Craig Cowan, Perturbations of Lane-Emden and Hamilton-Jacobi equations I: the full space case, Nonlinear Analysis, 151 (2017), 227-251.
  • S. Ai and Craig Cowan, Perturbations of Lane–Emden and Hamilton–Jacobi equations II: Exterior domains, J. Diff. Equations, 260 (2016), 8025--8050.
  • S. Ai and Zhian Wang, Traveling Waves for the Keller-Siegel Model with Population Growth, Mathematical Biosciences and Engineering, 12 (2015), 717-737.
  • S. Ai, Wenzhang Huang and Zhian Wang, Traveling wave solutions to a chemotaxis system with logistic growth, Discrete and Continuous Dynamical Systems – Series B, 20 (2015), 1-21.
  • Liming Cai, S. Ai and Jia Li, Dynamics of mosquitoes populations with different strategies of releasing sterile mosquitos, SIAM, J. Appl. Math., 74 (2014), 1786-1809.
  • S. Ai and Reem Albashaireh, Traveling waves in spatial SIRS models, J. Dynam. Diff. Equat. 26 (2014), 143-164.
  • S. Ai, Jia Li and Juliang Lu, Mosquito-stage-structured malaria models and their global dynamics, SIAM J. Appl. Math., 72 (2012), 1223-1237.
  • S. Ai, Self-similar solutions with fat tails for a nonlocal coagulation equation, Nonlinearity, 23 (2010), 579-587.
  • S. Ai, Traveling waves in a model of a fungal disease over a vineyard, SIAM. J. Math. Anal., 42 (2010), 833-856.
  • S. Ai, Spatially periodic patterns for nonlocal reaction-diffusion equations, Applicable Analysis, 89 (2010), 963-981.
  • S, Ai, Traveling waves in modeling of aerosolized skin grafts, Physica D: Nonlinear Phenomena, 237 (2008), 2761-2766.
  • S. Ai and John Pelesko, Dynamics of a canonical electrostatic MEMS/NEMS, J. Dynam. Diff. Eqns. 20 (2008), 609-641.
  • S. Ai, Traveling waves in a bioremediation model, SIAM J. Appl. Math. 68 (2007/2008), 680-693.
  • S. Ai, Global stability of equilibria in a tick-borne disease model, Math. Biosci. Eng. 4 (2007), 567-572.
  • S. Ai and Wenzhang Huang, Traveling wave fronts in combustion and chemical reaction models, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 671-700.
  • S. Ai, Traveling wave fronts for generalized Fisher equations with spatial-temporal delays, J. Diff. Eqns. 232 (2007), 104-133.
  • S. Ai, Xinfu Chen and Stuart Hastings, Layers and spikes in non-homogeneous bistable reaction-diffusion equations, Trans. Amer. Math. Soc. 358 (2006), 3169- 3206.
  • S. Ai and Wenzhang Huang, Traveling waves for a reaction-diffusion system in population dynamics and Epidemiology, Proc. Roy. Soc. Edinburgh Sect. A (2005), 663-676.
  • S. Ai, Homoclinic solutions to the Gray-Scott model, Appl. Math. Lett. 17 (2004), 1357-1361.
  • S. Ai, Multiple Positive Periodic Solutions for a delay host macroparasite model, Commun. Pure Appl. Anal. 3 (2004), 175-182.
  • S. Ai, Shui-Nee Chow and Yingfei Yi, Traveling wave solutions in a tissue interaction model for skin pattern formation, J. Dynam & Diff Eqns. 15 (2003), 517-534.
  • S. Ai, Existence of traveling wave solutions in a tissue interaction model for skin pattern formation, J. Nonlinear Sci. 13 (2003), 449-470.
  • S. Ai, Multi-bump solutions to Carrier's problem, J. Math. Anal. Appl. 277 (2003), 405-422.
  • S. Ai and Stuart Hastings, A shooting approach to layers and chaos in a forced Duffing equation, J. Diff. Eqns. 185 (2002), 389-436.
  • S. Ai, Multi-pulse like orbits for a singularly perturbed nearly-integrable system, J. Diff. Eqns. 179 (2002), 384-432.
  • S. Ai, Asymptotic formula for solutions of linear delay difference systems, J. Math. Anal. Appl. 264 (2001), 206-229.
  • S. Ai, Periodic Solutions in a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor, J. Math. Biol. 42 (2001), 71-94.
  • S. Ai and Xinfu Chen, Solutions of the two-dimensional 3-component gauged sigma model, J. Diff. Eqns. 153 (1999), 61-81.
  • S. Ai, Asymptotic integration of delay differential systems, J. Math. Anal. Appl. 165 (1992), 71-101.