Research Interest

My research interest lies in qualitative properties of nonlinear parabolic equations and systems, and about 40 papers have been published. 

We has obtained some subtle results on the critical blowup exponent, global existence, finite time blowup, global blowup for nonlocal problems, gradient blowup analysis.

In recent years, we pay much attention to the global existence, asymptotic behavior, finite time blowup for Keller-Segel equations, and has published about 10 papers.

Publications

Li, Yan; Li, Yuxiang; Global boundedness of solutions for the chemotaxis-Navier–Stokes system in R2. J. Differential Equations 261 (2016), no. 11, 6570–6613.

Zhang, Qingshan; Li, Yuxiang An attraction-repulsion chemotaxis system with logistic source. ZAMM Z. Angew. Math. Mech. 96 (2016), no. 5, 570–584.

Li, Yan; Li, Yuxiang Blow-up of nonradial solutions to attraction–repulsion chemotaxis system in two dimensions. Nonlinear Anal. Real World Appl. 30 (2016), 170–183.

Zhang, Qingshan; Li, Yuxiang Boundedness in a quasilinear fully parabolic Keller-Segel system with logistic source. Z. Angew. Math. Phys. 66 (2015), no. 5, 2473–2484.

Zhang, Qingshan; Li, Yuxiang Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system. Discrete Contin. Dyn. Syst. Ser. B 20 (2015), no. 8, 2751–2759.

Zhang, Qingshan; Li, Yuxiang Stabilization and convergence rate in a chemotaxis system with consumption of chemoattractant. J. Math. Phys. 56 (2015), no. 8, 081506, 10 pp.

Zhang, Qingshan; Li, Yuxiang Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusion. J. Differential Equations 259 (2015), no. 8, 3730–3754.

Wang, Wenjia; Li, Yuxiang Stabilization in an n-species chemotaxis system with a logistic source. J. Math. Anal. Appl. 432 (2015), no. 1, 274–288.

Zhang, Qingshan; Li, Yuxiang Global boundedness of solutions to a two-species chemotaxis system. Z. Angew. Math. Phys. 66 (2015), no. 1, 83–93.

Li, Yan; Li, Yuxiang Finite-time blow-up in higher dimensional fully-parabolic chemotaxis system for two species. Nonlinear Anal. 109 (2014), 72–84.

Zhang, Qingshan; Li, Yuxiang Global existence and asymptotic properties of the solution to a two-species chemotaxis system. J. Math. Anal. Appl. 418 (2014), no. 1, 47–63.

Liu, Xiaopan; Li, Yuxiang On the stability of global solutions to the 3D Boussinesq system. Nonlinear Anal. 95 (2014), 580–591.

Liang, Fei; Liu, Qi Lin; Li, Yu Xiang On a nonlocal problem modelling Ohmic heating in planar domains. Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 3, 523–534.

Li, Yuxiang; Wen, Xuefei Existence of multi-bump solutions for coupled Schrödinger systems. J. Southeast Univ. (English Ed.) 28 (2012), no. 4, 496–501.

Li, Yuxiang Optimal conditions for a priori estimates for semilinear elliptic systems with two components. Nonlinear Anal. 72 (2010), no. 3-4, 1850–1864.

Li, Yuxiang; Souplet, Philippe Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equations in planar domains. Comm. Math. Phys. 293 (2010), no. 2, 499–517.

Li, Yuxiang Stabilization towards the steady state for a viscous Hamilton-Jacobi equation. Commun. Pure Appl. Anal. 8 (2009), no. 6, 1917–1924.

Fei, Liang; Yuxiang, Li Blow-up for a nonlocal parabolic equation. Nonlinear Anal. 71 (2009), no. 7-8, 3551–3562.

Qilin, Liu; Fei, Liang; Li, Yuxiang Asymptotic behaviour for a non-local parabolic problem. European J. Appl. Math. 20 (2009), no. 3, 247–267.

Li, Yuxiang Optimal conditions for L∞-regularity and a priori estimates for semilinear elliptic systems. J. Math. Anal. Appl. 351 (2009), no. 1, 257–276.

Wang, Xianchao; Li, Yuxiang Asymptotical behavior of a nonlocal hyperbolic problem. Far East J. Dyn. Syst. 10 (2008), no. 2, 153–167.

Liu, Qilin; Li, Yuxiang; Gao, Hongjun Uniform blow-up rate for diffusion equations with nonlocal nonlinear source. Nonlinear Anal. 67 (2007), no. 6, 1947–1957.

Liu, Qilin; Li, Yuxiang; Gao, Hongjun Uniform blow-up rate for a nonlocal degenerate parabolic equations. Nonlinear Anal. 66 (2007), no. 4, 881–889.

Liu, Qi Lin; Li, Yu Xiang; Gao, Hong Jun Blow-up property for a reaction-diffusion system with nonlocal sources. (Chinese) Acta Math. Sinica (Chin. Ser.) 49 (2006), no. 4, 869–882.

Liu, Qilin; Li, Yuxiang; Gao, Hongjun Uniform blow-up rate for diffusion equations with localized nonlinear source. J. Math. Anal. Appl. 320 (2006), no. 2, 771–778.

Zou, Xiao Rong; Li, Yao Wen; Li, Yu Xiang The first eigenvalue λ1,p of the p-Laplace operator. Nihonkai Math. J. 16 (2005), no. 2, 129–133.

Li, Yuxiang; Wu, Jichun Extinction for fast diffusion equations with nonlinear sources. Electron. J. Differential Equations 2005, no. 23, 7 pp. (electronic).

Li, Yuxiang; Xie, Chunhong Blow-up for semilinear parabolic equations with nonlinear memory. Z. Angew. Math. Phys. 55 (2004), no. 1, 15–27.

Deng, Weibing; Li, Yuxiang; Xie, Chunhong A nonlinear degenerate parabolic system with non-local source and crosswise-diffusion. Z. Angew. Math. Phys. 54 (2003), no. 3, 503–516.

Liu, Qi Lin; Li, Yu Xiang; Xie, Chun Hong Blow-up of solutions to a degenerate parabolic equation with localized nonlinear reactions. (Chinese) Acta Math. Sinica (Chin. Ser.) 46 (2003), no. 6, 1135–1142.

Li, Yuxiang; Xie, Chunhong Quasilinear parabolic systems of several components. Math. Ann. 327 (2003), no. 2, 395–407.

Deng, Weibing; Yuxiang, Li; Chunhong, Xie Global existence and nonexistence for a class of degenerate parabolic systems. Nonlinear Anal. 55 (2003), no. 3, 233–244.

Deng, Weibing; Li, Yuxiang; Xie, Chunhong Semilinear reaction-diffusion systems with nonlocal sources. Math. Comput. Modelling 37 (2003), no. 9-10, 937–943.

Deng, Weibing; Li, Yuxiang; Xie, Chunhong Existence and nonexistence of global solutions of some nonlocal degenerate parabolic equations. Appl. Math. Lett. 16 (2003), no. 5, 803–808.

Li, Yuxiang; Xie, Chunhong Blow-up for p-Laplacian parabolic equations. Electron. J. Differential Equations 2003, No. 20, 12 pp. (electronic).

Deng, Weibing; Li, Yuxiang; Xie, Chunhong Blow-up and global existence for a nonlocal degenerate parabolic system. J. Math. Anal. Appl. 277 (2003), no. 1, 199–217.

Li, Yuxiang; Liu, Qilin; Xie, Chunhong Semilinear reaction-diffusion systems of several components. J. Differential Equations 187 (2003), no. 2, 510–519.

Deng, Weibing; Li, Yuxiang; Xie, Chunhong Existence and nonexistence of global solutions of some non-local degenerate parabolic systems. Proc. Amer. Math. Soc. 131 (2003), no. 5, 1573–1582.

Li, Yuxiang; Deng, Weibing; Xie, Chunhong Global existence and nonexistence from degenerate parabolic systems. Proc. Amer. Math. Soc. 130 (2002), no. 12, 3661–3670.