Professor Yihong Du

Professor of Mathematics - School of Science & Technology

Yihong Du

Phone: +61 +61 2 6773 3066

Email: ydu@une.edu.au

Biography

I obtained my PhD in 1988 from Shandong University (China). I joined UNE in 1991, firstly as a postdoctoral research fellow working with Prof. E.N. Dancer on an ARC supported project. While at UNE, I visited Heriot-Watt University (UK) under an Australian Academy of Science and the Royal Society exchange fellowship (1996), visited the Chinese Academy of Science under two Australian Academy of Science exchange fellowships (1999, 2001), visited the University of Tokyo and Waseda University under an Australian Academy of Science and JSPS fellowship (2006), and visited the Institute of Mathematics and Applications at the University of Minnesota as a long term visitor (2012). I also visited the National Center of Theoretical Sciences of Taiwan as a visiting professor (2002, 2007). I was an Adjunct Professor of Qufu Normal University (China) during 2004-2010.

Qualifications

MSc, PhD(Shandong University)

Teaching Areas

  • Calculus
  • Linear algebra
  • Real and complex analysis
  • Differential equations
  • Functional analysis

Research Interests

My research concerns mainly with nonlinear elliptic and parabolic equations and nonlinear functional analysis. My current research interest focuses on the existence, uniqueness and qualitative properties of solutions of various nonlinear partial differential equations, mostly arising from applied sciences, such as mathematical biology, invasion ecology and chemical reaction theory.

I've been the principal supervisor of several PhD and Master's degree students. For scholarship opportunities, see Postgraduate Scholarships.

 Major Research Grants

  • Y. Du, ARC discovery grant (DP150101867), 2015-2018:
    Propagation described by partial differential equations with free boundary.
  • S. Yan, E.N. Dancer and Y. Du, ARC discovery grant (DP130102773), 2013-2015:
    Singularity, degeneracy and related problems in nonlinear partial differential equations.
  • Y. Du, ARC discovery grant (DP120100727), 2012-2014:
    Propagation and free boundary problems in nonlinear partial differential equations.
  • Y. Du, E.N. Dancer and S. Yan, ARC discovery grant (DP1093638), 2010-2012:
    Transitions and singular behavior in nonlinear partial differential equations.

Publications

 Selected Publications

Du, Yihong; Poláčik, Peter, Locally uniform convergence to an equilibrium for nonlinear parabolic equations on RN. Indiana Univ. Math. J. 64 (2015) , 787–824.

Du, Yihong; Matsuzawa, Hiroshi; Zhou, Maolin, Spreading speed and profile for nonlinear Stefan problems in high space dimensions. J. Math. Pures Appl. 103 (2015), 741–787.

Du, Yihong; Matano, Hiroshi; Wang, Kelei, Regularity and asymptotic behavior of nonlinear Stefan problems. Arch. Ration. Mech. Anal.212 (2014),  957–1010.

Du, Yihong; Guo, Zongming; Wang, Kelei, Monotonicity formula and ε-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions. Calc. Var. Partial Differential Equations 50 (2014), 615–638.

Du, Yihong; Guo, Zongming; Peng, Rui, A diffusive logistic model with a free boundary in time-periodic environment. J. Funct. Anal.265 (2013), no. 9, 2089–2142.

Du, Yihong; Ma, Li, A Liouville theorem for conformal Gaussian curvature type equations in R2. Calc. Var. Partial Differential Equations 43 (2012), no. 3-4, 485–505.

Dancer, E. N.; Du, Yihong; Guo, Zongming,  Finite Morse index solutions of an elliptic equation with supercritical exponent. J. Differential Equations250 (2011), no. 8, 3281–3310.

Du, Yihong; Mei, Linfeng, On a nonlocal reaction-diffusion-advection equation modelling phytoplankton dynamics. Nonlinearity24 (2011), no. 1, 319–349.

Du, Yihong; Hsu, Sze-Bi, On a nonlocal reaction-diffusion problem arising from the modeling of phytoplankton growth. SIAM J. Math. Anal.42 (2010), no. 3, 1305–1333.

Cîrstea, Florica C.; Du, Yihong, Isolated singularities for weighted quasilinear elliptic equations. J. Funct. Anal. 259 (2010), 174–202.

Du, Yihong; Matano, Hiroshi, Convergence and sharp thresholds for propagation in nonlinear diffusion problems. J. Eur. Math. Soc. (JEMS) 12 (2010), 279–312.

Du, Yihong; Lin, Zhigui, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary. SIAM J. Math. Anal. 42 (2010), no. 1, 377–405.

Related Links

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