Dr. Shangbing Ai Associate Professor, Mathematical Sciences Department Education Ph.D., University of Pittsburgh, 1999 Classes Taught MA 171 - Calculus A MA 172 - Calculus B MA 201 - Calculus C MA 238 - Applied Differential Equations MA 324 - Applied Differential Equations MA 330 - Foundation of Mathematics MA 452/502 - Introduction to Real Analysis MA 458/508 - Applied Linear Algebra MA 453/503 - Intro to Complex Analysis MA 456/506 - Method of Partial Differential Equations MA 460/561 - Introduction to Fourier Analysis MA 524 - Dynamical Systems I MA 526 - Partial Differential Equations I MA 538 - Metric Spaces MA/PH 607 - Mathematical Physics I MA/PH 609 - Mathematical Physics II MA 624 - Dynamical Systems II MA 626 - Partial Differential Equations II MA 653 - Real Analysis I MA 654 - Real Analysis II MA 656 - Complex Analysis MA 662 - Asymptotics and Perturbation Theory MA 726 - Theory of Partial Differential Equations MA 799 - Doctoral Dissertation Publications S. Ai and C. Cowan, Critical elliptic equations via a dynamical systems approach. Nonlinear Anal. 182 (2019), 97–112. (PDF) L. Cai, S. Ai and F. Gui, Dynamics of delayed mosquitoes populations models with two different strategies of releasing sterile mosquitoes. Math. Biosci. Eng. 15 (2018), 1181-1202. (PDF) S. Ai, Yihong Du and Peng Rui, Traveling wave solutions for a Holling-Tanner predator-prey model, J. Diff. Equations, 263 (2017), 7782-7814. (PDF) 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.