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). After spending two years at Shandong University as a Lecturer (1988-90), and one year at Heriot-Watt University (UK) as a visiting fellow (1990-91), I joined UNE in 1991, as a postdoctoral research fellow (1991-92) working with Prof. E.N. Dancer on an ARC supported project. I became a Lecturer at UNE in 1993 and was promoted to a Professor in 2008. 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

BSc, MSc, PhD (Shandong University)

Awards

  • Clarivate (Web of Science) Highly Cited Researcher, 2018, 2019.
  • University Distinguished Speaker, University of Alabama in Huntsville, Jan.  2018.
  • Member of Australian Research Council’s College of Experts, 2013-2017, 2020-2022.
  • Eight Discovery Grants from the Australian Research Councile  (2003, 2007, 2010, 2012, 2013, 2015, 2017, 2019).
  • Vice-Chancellor’s Award for Excellence in Research, Univ.  of New England, 2007.
  • Four Exchange Grants from the Australian Academy of Science  (1996, 1999, 2001, 2006).
  • Sino-British Friendship Scholarship, 1990.

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 with nonlinear elliptic and parabolic equations and nonlinear functional analysis. My current research interest focuses on the 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.

Publications

Selected Publications

Y. Du and Wenjie Ni, Analysis of a West Nile virus model with nonlocal diffusion and free boundaries, Nonlinearity, to appear.

Y. Du, Fernando Quiros and Maolin Zhou, Logarithmic corrections in Fisher-KPP type porous medium equations, J. Math. Pure Appl., 136 (2020), 415-455.

Y. Du, Bendong Lou, Rui Peng and Maolin Zhou, The Fisher-KPP equation over simple graphs: Varied persistence states in river networks, J. Math. Biol, 80 (2020), 1559-1616.

Jiafeng Cao, Y. Du, Fang Li and Wan-Tong Li, The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries, J. Functional Anal., 277 (2019), 2772-2814.

Weiwei Ding, Y. Du and Xing Liang, Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed, AIHP Analyse non Lineaire, 36 (2019), 1539-1573.

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

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 and Xing Liang, Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model, Ann. Inst. Henri Poincare Anal. Non Lineaire, 32(2015), 279-305.

Y. Du and Bendong Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17(2015), 2673-2724.

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

Y. Du and Peter Polacik, Locally uniform convergence to an equilibrium for nonlinear parabolic equations on R^N, Indiana Univ. Math. J., 64(2015), 787-824.

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.

Dancer, E. N.; Du, Yihong; Guo, Zongming, Finite Morse index solutions of an elliptic equation with supercritical exponent. J. Differential Equations, 250 (2011), no. 8, 3281–3310.

Du, Yihong; Mei, Linfeng, On a nonlocal reaction-diffusion-advection equation modelling phytoplankton dynamics. Nonlinearity, 24 (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.

Memberships

Member of the Australian Mathematical Society.