Research


My research area is partial differential equations and its applications, which consist of two parts, one is the theoretical analysis and the other is numerical analysis, including simulations and scientific computations. I am interested in the global existence and blow-up solutions of the time dependent partial differential equations, mathematical modeling and applications related to ordinary and partial differential equations, such as reaction-diffusion equations, traveling waves, soliton and shock waves, radar beams and heat transfer and fluid dynamics. My research interests also include the numerical approximation in wireless communication areas to model and analyze the characteristics of various wireless systems. The following topics are my research work:

Nonlinear Parabolic Equations

Papers:

  1. Boundedness and blowup for nonlinear degenerate parabolic equations. Nonlinear Anal. 70 (2009), no. 2, 1087--1095.
  2. Boundedness and blowup solutions for quasilinear parabolic systems with lower order terms. Commun. Pure Appl. Anal. 8 (2009), no. 2, 587--600.
  3. Global existence and nonexistence for some degenerate and quasilinear parabolic systems. J. Differential Equations, 245 (2008), no. 4, 1112--1136.
  4. Global existence and blowup solutions for quasilinear parabolic equations. J. Math. Anal. Appl. 335 (2007), no. 1, 151--167 (with Deming Yu)
  5. A sufficient condition for blowup solutions of nonlinear heat equations. J. Math. Anal. Appl. 293 (2004), no. 1, 227--236.
  6. Global existence and blowup of solutions for a parabolic equation with a gradient term., Proc. Amer. Math. Soc., 129 (2001), no. 4, 975--981.

Numerical Approximation in Wireless Communuications

Paper:

  1. Lognormal Sum Approximation with a Variant of Type IV Pearson Distribution, Communications Letters, IEEE Volume 12, Issue 9, September 2008 Page(s): 630 - 632 (with Hong Nie and Nen Ayers-Glassey)
  2. Lognormal Sum Approximation with Type IV Pearson Distribution, IEEE Communications Letters, 11(2007), 790-792. (with Hong Nie).
  3. On the Receiving Power Pattern for Cellular CDMA Systems Employing Successive Interference Cancellation Personal, Indoor and Mobile Radio Communications, 2007. PIMRC 2007. IEEE 18th International Symposium on 3-7 Sept. 2007 Page(s):1 - 5 (with Hong Nie and Jacek Ilow).
  4. Statistical Characteristics of Reverse Link Inter-cell Interference for Cellular CDMA Systems with Random Power Disparities, IEEE EIT 2007 Proceedings, 289 ¨C 294 (with Hong Nie and Jacek Ilow).

Moving Mesh Methods

Paper:

  1. Comparison of Some Moving Mesh Methods in Higher Dimensions, Advances on Scientific Computing and Applications, Science Press, Beijing/New York, 2004, pp 117-132 (with R. D. Russell and Wentao Sun).
  2. New self-similar solutions of the nonlinear Schrodinger equation with moving mesh computations J. Comput. Phys. 152 (1999), no. 2, 756--789 (with C. Budd and R. D. Russell).

Semilinear Elliptic Equations

Papers:

  1. Some properties for the solutions of a general activator-inhibitor model. Commun. Pure Appl. Anal. 5 (2006), no. 4, 919--928.
  • Existence and nonexistence of positive radial solutions for a class of semilinear elliptic system, Nonlinear Anal., 38 (1999), no. 7, Ser. A: Theory Methods, 919--932. (with Guozhen Lu)
  • Asymptotic behavior of radial solutions for a class of semilinear elliptic equations, J. Differential Equations, 133 (1997), no. 2, 340--354. (with Guozhen Lu)
  • Boundedness and blow up for the general activator-inhibitor model, Acta Math. Appl. Sinica (English Ser.), 11 (1995), no. 1, 59--68. (with Ming De Li and Yu Chun Qin)

    • A complete list of publications