Partial differential equations and their applications
January, 2016 Chair Professor, Southern University of Science and Technology
Fall 2015 Visiting Professor, Center for PDE, East China Normal Univ
Fall 2014 Visiting Professor, Center for PDE, East China Normal Univ
Spring 2011 Visiting Professor, Hong Kong Baptist Univ
2002-Jan, 2016 Professor, Tulane University
Fall 2004 Visiting Scholar, University of Minnesota and Air Force Institute of Technology
1996 - 2002 Associate Professor, Tulane University
Spring 1995 Visiting Scholar, University of Utah
1991 - 1996 Assistant Professor, Tulane University
1990 - 1991 Visiting Assistant Professor, Tulane University
July, 1990 Ph.D., School of Mathematics
University of Minnesota, Minneapolis, Minnesota
1984 - 1986 Graduate student, Department of Mathematics
Peking University, Beijing, China
1980 - 1984 B.S., Department of Mathematics
Peking University, Beijing, China
1. A remark on strong maximum principle for parabolic and elliptic systems, Proceedings of American Mathematical Society 109 (1990), 343-348.
2. Blow-up behavior of ground states of a semilinear elliptic equation in Rn involving critical Sobolev exponent (with X. Pan), Journal of Differential Equations 99 (1992), 78-107.
3. On the stability and instability of positive steady states of a semilinear heat equation in Rn (with C. Gui and W.-M. Ni), Communications on Pure and Applied Mathematics, Vol. XLV (1992), 1153-1181.
4. On concentration of positive bound states of nonlinear Schrödinger equations, Communications in Mathematical Physics 153 (1993), 229-244.
5. On the Cauchy problem for reaction-diffusion equations, Transactions of the American Mathematical Society 337 (1993), 549-589.
6. The critical asymptotics of scalar curvatures of the conformal complete metrics with negative curvature (with C. Gui), Duke Math. Journal 76 (1994), 293-302.
7. Life span of solutions of the Cauchy problem for a semilinear heat equation (with C. Gui), Journal of Differential Equations 115 (1995), 166-172.
8. On the equation u + k(x)u(n+2)/(n-2)± 2= 0 in Rn (with J. Wei), Rendiconti del Circolo Math. di Palermo, Serie II, Tomo XLIV (1995), 365-400.
9. On location of blow-up of ground states of semilinear elliptic equations in Rn involving critical Sobolev exponents, Journal of Differential Equations, 127 (1996), 148-173.
10. Traveling waves in a convolution model for phase transitions (with P. Bates, P. Fife and X. Ren), Archive for Rational Mechanics and Analysis 138 (1997), 105-136.
11. On concentration of positive bound states of nonlinear Schrödinger equations with competing potential functions (with B. Zeng), SIAM Journal on Mathematical Analysis 28 (1997), 633-655.
12. Semilinear Neumann problem on exterior domains (with X. Pan), Nonlinear Analysis 31 (1998), 791-821.
13. A convolution model for interfacial motion: the generation and propagation of internal layers in higher space dimensions (with P. Fife), Advances in Differential Equations, 3 (1998), 85-110.
14. Shift and stability of ground states of a nonlinear Schrödinger equation outside a small insulated domain (with J. Wei), in Journal of Differential Equations 154 (1999), 73-95.
15. Qualitative behavior of solutions of a chemotactic diffusion system: Effects of motility and chemotaxis and dynamics, SIAM Journal on Mathematical Analysis 31 (2000), 535-560.
16. Further study on a semilinear heat equation in Rn (with C. Gui and W.-M. Ni), Journal of Differential Equations 169 (2001), 588- 613.
17. Qualitative analysis on a chemotactic diffusion model for two species competing for a limited resource (with Y. Wu), Quarterly of Applied Mathematics, Vol LX (2002), 505-531.
18. Existence and nonexistence of entire positive solutions of semilinear elliptic systems (with A. Wood), Journal of Mathematical Analysis and Applications 267(2002), 361-368.
19. Metastability and stability of patterns in a convolution model for phase transitions, Journal of Differential Equations 183 (2002), 434-461.
20. Mass transport through swelling membranes (with Q. Liu and D. De Kee), International Journal of Engineering Science 43 (2005), 1464-1470.
21. Suppression of the Dirichlet eigenvalues of a coated body (with Steve Rosencrans), SIAM Journal on Applied Math 66(2006), 1839-2205.
22. Hair-triggered instability of radial steady states, spread and extinction in semilinear heat equations(with J. Shi), Journal of Differential Equations 231(2006), 235-251.
23. On the first positive Neumann eigenvalue (with Wei-Ming Ni) , Discrete and Continuous Dynamical Systems 17(2007), 1-19.
24. On global bifurcation for quasilinear elliptic systems on bounded domains(with J. Shi),Journal of Differential Equations 246 (2009), 2788-2812
25. Measuring the insulating ability of anisotropic thermal conductors via principal Dirichlet eigenvalue (with S. Rosencrans, B. Winter and S. Zhao ), European Journal of Applied Math 20(2009), 231-246.
26. Asymptotic analysis of Dirichlet problem for heat equation on a coated body(with J. Li, S. Rosencrans and K. Zhang), Proceedings of the American Mathematical Society 137(2009), 1711-1721.
27. Estimating the thermal insulating ability of anisotropic coatings via Robin eigenvalues and eigenfunctions (with G. Zhang, S. Rosencrans and K. Zhang), Discrete and Continuous Dynamical Systems 25(2009), 1061-1079.
28. On a Chemotaxis Model with Saturated Chemotactic Flux (Alina Chertock, A. Kurganov& Yaping Wu), Kinetic and Related Models 3 (2012), 51-95.
29. Asymptotic analysis of Robin problem for heat equation on a coated body (with J. Li, G. Zhang and K. Zhang), Rocky Mountain J Math. Volume 42(2012), 937-958.
30. Effective boundary conditions resulting from anisotropic and optimally aligned coatings: the two dimensional case (with Xinfu Chen & Cody Pond), Archive for Rational Mechanics and Analysis 206 (2012), pp. 911-951.
31. Estimating eigenvalues of an anisotropic thermal tensor from transient thermal probe measurements (with S. Rosencrans & Shan Zhao), Discrete and Continuous Dynamical Systems, Series A, 33 (2013), pp. 5441-5455.
32. Spiky and transition layer steady states of chemotaxis systems via global bifurcation method and Helly's compactness theorem (with Qian Xu), Journal of Mathematical Biology (2013), no. 6, 1241–1266.
33. The effective boundary conditions and their life span of the logistic heat equation on a coated body (with Huicong Li and Yanxia Wu), Journal of Diff Eq,, 257 (2014), 3640-3668.
34. Stability of Spiky Solution of the Keller-Segel’s Minimal Chemotaxis Model (with Xinfu Chen, Jianghao Hao, Yaping Wu, Yajing Zhang), Journal of Diff Eq., 257 (2014), 3102-3134.
John Stibbs Award for Outstanding Faculty Member, 2009, by The Graduate and Professional Student Association of Tulane University.