Professor Yihong Du

Professor of Mathematics - Faculty of Science, Agriculture, Business and Law; School of Science and Technology

Yihong Du

Phone: +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)

Awards

  • Clarivate (Web of Science) Highly Cited Researcher, 2018.
  • University Distinguished Speaker, University of Alabama in Huntsville, Jan.  2018.
  • Member of Australian Research Council’s College of Experts, 2013-2017.
  • Vice-Chancellor’s Award for Excellence in Research, Univ.  of New England, 2007.

Teaching Areas

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

Primary Research Area/s

Nonlinear elliptic and parabolic differential equations; Nonlinear functional analysis; Mathematical models in biology and spatial ecology

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 Grant

  • Y. Du, ARC  discovery  grant (DP190103757), 2019-2021: Propagation  via  nonlinear  partial  differential  equations.
  • S. Yan, E.N. Dancer, Y. Du and C.S. Lin, ARC discovery grant (DP170103087), 2017-2019: Nonlinear partial differential equations: bubbles, layers and stability.
  • 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.

Research Supervision Experience

Publications

Selected Publications

Y. Du and Chang-Hong Wu, Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries, Cal. Var. PDE, 57:52(2018), 36pages.

Y. Du, Lei Wei and Ling Zhou, Spreading in a shifting environment modelled by the diffusive logistic equation with a free boundary, J. Dyn.  Diff. Equations, 30(2018), 1389-1426

Wendi Bao, Y. Du, Zhigui Lin and Huaiping Zhu, Free boundary models for mosquito range movement driven by climate warming, J. Math. Biology, 76 (2018), 841-875.

Y. Du, Mingxin Wang and Maolin Zhou, Semi-wave and spreading speed for the diffusive competition model with a free boundary, J. Math. Pure Appl., 107(2017), 253-287.

Y. Du, Bendong Lou and Maolin Zhou, Nonlinear diffusion problems with free boundaries: Convergence, transition speed and zero number arguments, SIAM J. Math. Anal., 47(2015), 3555-3584.

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.

Clinical Skills and Experience

Memberships

Member of the Australian Mathematical Society.

Consultancy Interests

Community and Advocacy Organisation Collaborations

External Profiles

Further Information