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
- Global existence for some parabolic equations and systems
- Blowup solutions for some parabolic equations and systems
- Boundedness and blowup for nonlinear degenerate parabolic equations.
Nonlinear Anal. 70 (2009), no. 2, 1087--1095.
- Boundedness and blowup solutions for quasilinear parabolic systems
with lower order terms. Commun. Pure Appl. Anal. 8 (2009), no. 2, 587--600.
- Global existence and nonexistence for some degenerate and quasilinear
parabolic systems. J. Differential Equations, 245 (2008), no. 4, 1112--1136.
- Global existence and blowup solutions for quasilinear parabolic equations.
J. Math. Anal. Appl. 335 (2007), no. 1, 151--167 (with Deming Yu)
- A sufficient condition for blowup solutions of nonlinear heat equations.
J. Math. Anal. Appl. 293 (2004), no. 1, 227--236.
- 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
- Sum of lognormal random variables
- Type IV Pearson distribution
- Receiving Power Pattern for Cellular CDMA Systems
- 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)
- Lognormal Sum Approximation with Type IV Pearson Distribution,
IEEE Communications Letters, 11(2007), 790-792. (with Hong Nie).
- 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).
- Statistical Characteristics of Reverse Link Inter-cell Interference for
Cellular CDMA Systems with Random Power Disparities, IEEE EIT 2007
Proceedings, 289 ĘC 294 (with Hong Nie and Jacek Ilow).
Moving Mesh Methods
- Studies on the monitor functions
- Radially symmetric solutions and blowup properties
- Autometic rescaling properties
- 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).
- 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
- Existence and nonexistence of positive solutions
- Asymptotic behavior of radial solutions
- Oscillatory radial solutions
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)
- Some properties for the solutions of a general activator-inhibitor model.
Commun. Pure Appl. Anal. 5 (2006), no. 4, 919--928.
A complete list of publications