Publications since 2004:
Books
 Y. Du, Order structure and topological methods in nonlinear partial differential equations. Vol. 1. Maximum principles and applications. Series in Partial Differential Equations and Applications, 2. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006. (x+190 pages. ISBN: 9812566244)
 Y. Du, Hitoshi Ishii and WeiYueh Lin (eds.) Recent Progress in Nonlinear Partial Differential Equations and Viscosity Solutions, World Scientific Publishing, 2009. (372 pages. ISBN: 9812834737)
Papers
 Xin Long, Y. Du, Wenjie Ni and Taishan Yi, Dynamics of the nonlocal KPP equation: Effects of a new free boundary condition, submitted, 2024.
 Y. Du, Wenjie Ni and Linfei Shi, Longtime dynamics of a competition model with nonlocal diffusion and free boundaries, part 2: Chances of successful invasion, submitted, 2024.
 Y. Du, Wenjie Ni and Linfei Shi, Longtime dynamics of a competition model with nonlocal diffusion and free boundaries, part 1: Vanishing and spreading of the invader, submitted, 2024.
 Y. Du, Propagation dynamics of the monostable reactiondiffusion equation with a new free boundary condition, 2023, preprint.
 Huyuan Chen, Y. Du and Feng Zhou, Improved Leray inequality and TrudingerMoser type inequalities involving the Leray potential, 2023, submitted.
 Y. Du and Wenjie Ni, Exact rate of accelerated propagation in the FisherKPP equation with nonlocal diffusion and free boundaries, Math. Ann. (Published online Sept. 2023).
 Y. Du and Wenjie Ni, Spreading speed for some cooperative systems with nonlocal diffusion and free boundaries, part 2: Precise rates of spreading, 2023, submitted.
 Y. Du, Wenjie Ni and Rong Wang, Rate of accelerated expansion of the epidemic region in a nonlocal epidemic model with free boundaries, Nonlinearity, 36(2023), 56215660.
 JianWen Sun and Y. Du, Fine patterns for a nonlocal periodicparabolic equation with spatial degeneracy, J. Diff. Equations, 383 (2024), 7895.
 Y. Du and Wenjie Ni, The high dimensional FisherKPP nonlocal diffusion equation with free boundary and radial symmetry, Part 2, 2022, submitted.
 Shangbing Ai, Y. Du, Yujuan Jiao and Rui Peng, Traveling wave solutions of a class of multispecies noncooperative reactiondiffusion systems, Nonlinearity, 36 (2023), 23712402.
 Y. Du and Wenjie Ni, Rate of propagation for the FisherKPP equation with nonlocal diffusion and free boundaries, J. European Math. Soc. (Published online Dec. 2023 )
 Zhiguo Wang, Hua Nie and Y. Du, Sharp asymptotic profile of the solution to a West Nile virus model with free boundary, Europ. J. Appl. Math., to appear.
 Y. Du and Wenjie Ni, The FisherKPP nonlocal diffusion equation with free boundary and radial symmetry in R^3, 2022, Math. Engineering (special issue dedicated to Prof N.S. Trudinger), 5 (2) (2023), 126. (Published online June 2022)
 Rong Wang and Y. Du, Longtime dynamics of a nonlocal epidemic model with free boundaries: spreading speed, Disc. Con. Dynam. Syst.  A, 43 (2023), 121161.
 Y. Du, Jian Fang and Ningkui Sun, A deley induced nonlocal free boundary problem, Math. Ann.,386 (2023), 20612106. (Published online Aug. 2022)
 Rong Wang and Y. Du, Longtime dynamics of a nonlocal epidemic model with free boundaries: spreadingvanishing dichotomy, J. Diff. Equations, 327 (2022), 322381.
 Y. Du, Propagation and reaction diffusion models with free boundaries,(expository article), Bull. Math. Sci., 12 (1) (2022), 2230001, 56pp.
 Y. Du and ChangHong Wu, Classification of the spreading behaviors of a twospecies diffusioncompetition system with free boundaries, Cal. Var. PDE, 61:54 (2022), 34 pages.
 TingYing Chang and Y. Du, Longtime dynamics of an epidemic model with nonlocal diffusion and free boundaries, Electronic Research Archive (ERA), 30 (2022), 289313.
 Y. Du and Wenjie Ni, The high dimensional FisherKPP nonlocal diffusion equation with free boundary and radial symmetry, Part 1, SIAM J. Math. Anal., 54 (2022), No. 3, 39303973.
 K. Khan, T.M. Schaerf and Y. Du, Effects of environmental heterogeneity on species spreading via numerical analysis of some free boundary models, DCDSB (special issue dedicated to the memory of Prof. M. Mimura), 28 (2023), 62486288.
 Y. Du, Alejandro Garriz and Fernando Quiros, Travellingwave behaviour in doubly nonlinear reactiondiffusion equations, preprint, 2020.
 Y. Du and Wenjie Ni, Spreading speed for some cooperative systems with nonlocal diffusion and free boundaries, part 1: Semiwave and a threshold condition, J. Diff. Eqns., 308 (2022), 369420.
 Y. Du, Yuanyang Hu and Xing Liang, A climate shift model with free boundary: Enhanced invasion, J. Dyn. Diff. Equations, 35(2023), 771–809. (published online June 2021).
 Rong Wang and Y. Du, Longtime dynamics of a diffusive epidemic model with free boundaries, DCDSB (special issue dedicated to Prof S.B. Hsu), 26 (2021), 22012238.
 Y. Du, Propagation, diffusion and free boundaries, (Review article, dedicated to Prof Dajun Guo's 85th birthday), SN Partial Differ. Equ. Appl. (2020) 1:35.
 K. Khan, Shuang Liu, T.M. Schaerf and Y. Du, Invasive behaviour under
competition via a free boundary model: A numerical
approach, J. Math. Biol. 83 (2021):23, 43 pages. (Published Aug. 5, 2021)
 Y. Du, Changfeng Gui, Kelei Wang and Maolin Zhou, Semiwaves with $\Lambda$shaped free boundary for nonlinear Stefan problems: Existence, Proc. Amer. Math. Soc., 149(2021), 2091–2104.
 Y. Du, Wantong Li, Wenjie Ni and Meng Zhao, Finite or infinite spreading speed of an epidemic model with free boundary and double nonlocal effects, J. Dynam. Diff. Eqns. (Published online May 2022).
 Y. Du and Wenjie Ni, Approximation of random diffusion equation by nonlocal diffusion equation in free boundary problems of one space dimension, Comm. Contemp. Math. 25(4) (2023), 2250004, 42pages. (Published online April 2022) (arXiv:2003.05560)
 Meng Zhao, WanTong Li and Y. Du, The effect of nonlocal reaction in an epidemic model with nonlocal diffusion and free boundaries, Comm. Pure Appl. Anal., 19(2020), 45994620.
 Yuanyang Hu, Xinan Hao and Yihong Du, Spreading under shifting climate by a free boundary model: Invasion of deteriorated environment, Comm. Contemp. Math., 23 (2021): 2050077, 49 pages. (published online Dec 3, 2020)
 Meng Zhao, Yang Zhang, WanTong Li and Y. Du, The dynamics of a degenerate epidemic model with nonlocal diffusion and free boundaries, J. Diff. Eqns, 269(2020), 33473386.
 Y. Du and Wenjie Ni, Analysis of a West Nile virus model with nonlocal diffusion and free boundaries, Nonlinearity, 33(2020), 44074448.
 Y. Du, Fang Li and Maolin Zhou, Semiwave and spreading speed of the nonlocal FisherKPP equation with free boundaries, J. Math. Pure Appl., 154(2021), 3066. (arXiv: 1909.03711).
 Yuanyang Hu, Xinan Hao, Xianfa Song and Y. Du, A free boundary problem for spreading under shifting climate, J. Diff. Equations, 269 (2020), 59315958.(arXiv: 1908.04041)
 Maud ElHachem, Scott W. McCue, Wang Jin, Yihong Du, Matthew J. Simpson, Revisiting the FisherKPP equation to interpret the spreadingextinction dichotomy, Proc. Royal Soc. A, 475 (2019), no. 2229, article id: 20190378.
 Y. Du, Mingxin Wang and Meng Zhao, Two species nonlocal diffusion systems with free boundaries, DCDSA, 42 (2022), 11271162. (arXiv:1907.04542)
 Zhiguo Wang, Hua Nie and Y. Du, Spreading speed for a West Nile virus model with free boundary, J. Math. Biol., 79(2019), 433466.
 Y. Du, Bendong Lou, Rui Peng and Maolin Zhou, The FisherKPP equation over simple graphs: Varied persistence states in river networks, J. Math. Biol, 80 (2020), 15591616.(published online Jan. 2020). (arXiv:1809.06961)
 Y. Du, On the work of Norman Dancer, Disc. Cont. Dyn. SystS, 12 (2019), 18071833.
 Jiafeng Cao, Y. Du, Fang Li and WanTong Li, The dynamics of a FisherKPP nonlocal diffusion model with free boundaries, J. Functional Anal., 277 (2019), 27722814. ( Published online Feb. 2019)
 Y. Du, Fernando Quiros and Maolin Zhou, Logarithmic corrections in FisherKPP type porous medium equations, J. Math. Pure Appl., 136 (2020), 415455. (published online Dec. 2019) (arXiv:1806.02022)
 Lei Wei and Y. Du, Positive solutions of elliptic equations with a strong singular potential, Bull. London Math Soc, 51(2019), 251266.
(published online Dec 2018).
 Weiwei Ding, Y. Du and Zongming Guo, The Stefan problem for the FisherKPP equation with unbounded initial range, Cal. Var. PDEs 60:69 (2021), 37 pages. (arXiv:2003.10100)
 Shuang Liu, Y. Du and Xinfeng Liu, Numerical methods for a class of reactiondiffusion equations with free boundaries, International J. Computer Math., 97(2020), 959979.
 Zhiguo Wang, Hua Nie and Y. Du, Asymptotic spreading speed for the weak competition system with a free boundary, DCDSA, 39(2019), 52235262.(arXiv1710.05485)
 Chengxia Lei, Hua Nie, Wei Dong and Y. Du, Spreading of two competing species governed by a free boundary model in a shifting environment, J. Math. Anal. Appl., 462(2018), 12541282. (Published online Feb. 2018).
 Y. Du and Messoud Efendiev, Existence and exact multiplicity for quasilinear elliptic equations in quarterspaces, In: Gurevich P., Hell J., Sandstede B., Scheel A. (eds) "Patterns of Dynamics", pp. 128137. Springer Proceedings in Mathematics & Statistics, vol 205. Springer, 2016.
 Y. Du and Hiroshi Matano, Radial terrace solutions and propagation profile of multistable reactiondiffusion equations over R^N, submitted, 2017.(arXiv 1711.00952)
 Y. Du and ChangHong Wu, Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries, Cal. Var. PDE, 57:52(2018), 36pages.(arXiv 1710.05482)
 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), 841875. (published online July 2017).
 Weiwei Ding, Y. Du and Xing Liang, Spreading in spacetime periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed, AIHP Analyse non Lineaire, 36 (2019), 15391573.(Published online Jan. 2019)
 Weiwei Ding, Y. Du and Xing Liang, Spreading in spacetime periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions, J. Diff. Eqns., 262(2017), 49885021. (arXiv1611.01909)
 Y. Du, Bendong Lou and Maolin Zhou, Spreading and vanishing for nonlinear Stefan problems in high space dimensions, J. Elliptic and Parabolic Equations, 2 (2016), 297321.
 Shangbing Ai, Y. Du and Rui Peng, Traveling waves for a generalized HollingTanner predatorprey model, J. Diff. Equations, 263(2017), 77827814.
 Xuemei Zhang and Y. Du, Sharp conditions for the existence of boundary blowup solutions to the MongeAmpere equation, Cal. Var. PDEs, 57:30(2018), 24pages.

Chengxia Lei and Y. Du, Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model, Discrete Cont. Dyn. Syst. B (special issue for Stephen Cantrell), 22(2017), 895911.

Y. Du, Mingxin Wang and Maolin Zhou, Semiwave and spreading speed for the diffusive competition model with a free boundary, J. Math. Pure Appl., 107(2017), 253287. (arXiv1505.07689)

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), 13891426 (published online Aug. 2017).(arXiv1508.06246)
 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), 35553584.(arXiv1501.06258)
 Y. Du and L. Wei, Boundary behavior of positive solutions to nonlinear elliptic equations with Hardy potential, J. London Math. Soc., 91(2015), 731749.
 L. Wei and Y. Du, Exact singular behavior of positive solutions to nonlinear elliptic equations with a Hardy potential, J. Diff. Eqns., 262(2017), 38643886.
 Y. Du and Zongming Guo, Finite Morse index solutions of weighted elliptic equations and the critical exponents, Calculus of Variations and PDEs, 54(2015), 31613181.
 Y. Du, S.B. Hsu and Yuan Lou, Multiple steadystates in phytoplankton population induced by phytoinhibition, J. Diff. Eqns, 258(2015), 24082434.
 Y. Du, Spreading profile and nonlinear Stefan problems, Bull. Inst. Math. Academia Sinica (Special Issue for Neil Trudinger), 8(2013), 413430.
 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), 741787. (PDF)
 P. AlvarezCaudevilla, Y. Du and Rui Peng, Qualitative analysis of a cooperative reactiondiffusion system in spatiotemporally degenerate environment, SIAM J. Math. Anal., 46(2014), 499531.
 Y. Du, Zongming Guo and Kelei Wang, Monotonicity formula and epsilonregularity of stable solutions to supercritical problems and applications to finite Morse index solutions, Calculus of Variations and PDEs, 50(2014), 615638.
 Y. Du and Zhigui Lin, The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor, Discrete Cont. Dyn. Syst.B (Special issue for Chris Cosner), 19(2014), 31053132. (arXiv1303.0454)
 Y. Du and Peter Polacik, Locally uniform convergence to an equilibrium for nonlinear parabolic equations on R^N, Indiana Univ. Math. J., 64(2015), 787824. (PDF)
 Y. Du, Hiroshi Matano and Kelei Wang, Regularity and asymptotic behavior of nonlinear Stefan problems, Arch. Rational Mech. Anal., 212(2014), 9571010. (PDF)
 Y. Du, Hiroshi Matsuzawa and Maolin Zhou, Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal., 46(2014), 375396. (PDF)
 Y. Du and Xing Liang, Pulsating semiwaves in periodic media and spreading speed determined by a free boundary model, Ann. Inst. Henri Poincare Anal. Non Lineaire, 32(2015), 279305. (PDF)
 Y. Du and R. Peng, Sharp spatiotemporal patterns in the diffusive timeperiodic logistic equation, J. Diff. Eqns., 254 (2013), 37943816.
 Y. Du, Establishment or vanishing: fate of an invasive species based on mathematical models, in "The Balance of Nature and Human Impact", edited by Klaus Rohde, Cambradge Univ Press, 2013, pp231238.
 Y. Du and Z.M. Guo, Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations, Adv. Diff. Eqns., 18(2013), 737768. (arXiv1303.4145)
 G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Networks and Heterogeneous Media (special issue dedicated to H. Matano), 7 (2012), 583603. (PDF file)
 E.N. Dancer, Y. Du and M. Efendiev, Quasilinear elliptic equations on half and quarterspaces, Adv. Nonlinear Studies (special issue dedicated to Klaus Schmitt), 13 (2013), 115136.
 Y. Du, Zongming Guo and Rui Peng, A diffusive logistic model with a free boundary in timeperiodic environment, J. Funct. Anal., 265 (2013), 20892142. (PDF file)
 Y. Du and Bendong Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17(2015), 26732724. (arXiv1301.5373)
 Y. Du and Z.M. Guo, The Stefan problem for the FisherKPP equation, J. Diff. Eqns., 253(2012), 9961035. (PDF file)
 Y. Du, Rui Peng and Peter Polacik, The parabolic logistic equation with blowup initial and boundary values, J. d'Analyse Math., 118 (2012), 297316.
 Y. Du and Linfeng Mei, On a nonlocal reactiondiffusionadvection equation modeling phytoplankton, Nonlinearity, 24(2011), 319349.
 Y. Du and Zongming Guo, Spreadingvanishing dichotomy in the diffusive logistic model with a free boundary II, J. Diff. Eqns., 250(2011), 43364366. (PDF file)
 F. Cirstea and Y. Du, Isolated singularities for weighted quasilinear elliptic equations, J. Functional Anal., 259(2010), 174202.
 Y. Du and Li Ma, A Liouville theorem for conformal Gaussian curvature type equations in $\R^2$, Calculus of Variations and PDEs, 43(2012), 485505.
 Y. Du and Zhigui Lin, Spreadingvanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42(2010), 377405. (PDF file) ERRATUM: SIAM J. Math. Anal., 45(2013), 19951996.
 Y. Du and S.B. Hsu, On a nonlocal reactiondiffusion problem arising from the modeling of phytoplankton growth, SIAM J. Math. Anal., 42(2010), 13051333.
 Y. Du and R. Peng, The periodic logistic equation with spatial and temporal degeneracies, Trans. Amer. Math. Soc., 364(2012), 60396070. (PDF file)
 E.N. Dancer, Y. Du and Zongming Guo, Finite Morse index solutions of an elliptic equation with supercritical exponent, J. Diff. Eqns., 250(2011), 32813310.
 Y. Du, Change of environment in model ecosystems: effect of a protection zone in diffusive population models, in "Recent Progress in Nonlinear Partial Differential Equations and Viscosity Solutions", Eds. Y. Du, H. Ishii and W.Y. Lin, World Scientific Publishing, 2009. ISBN 9789812834737
 Y. Du and Hiroshi Matano, Convergence and sharp thresholds for propagation in nonlinear diffusion problems, J. European Math. Soc., 12(2010), 279312. (PDF file)
 Y. Du, Rui Peng and Mingxin Wang, Effect of a protection zone in the diffusive Leslie predatorprey model, J. Diff. Eqns., 246(2009), 39323956.
 Y. Du, Zhaoli Liu, Angela Pistoia and Shusen Yan, Sign changing solutions with clustered layers near the origin for singularly perturbed semilinear elliptic problems on a ball, Methods and Applications of Analysis (special issure dedicated to N.S. Trudinger), 15(2008), 137148.
 Y. Du and Z.M. Guo, Positive solutions of an elliptic equation with negative exponent: stability and critical power, J. Diff. Eqns., 246(2009), 23872414.
 Y. Du and S.B. Hsu, Concentration phenomena in a nonlocal quasiliear problem modelling phytoplankton I: Existence, SIAM J. Math. Anal. 40(2008), 14191440.
 Y. Du and S.B. Hsu, Concentration phenomena in a nonlocal quasiliear problem modelling phytoplankton II: Limiting profile, SIAM J. Math. Anal. 40(2008), 14411470.
 Y. Du, P.Y.H. Pang and M. Wang, Qualitative analysis of a predatorprey model with stage structure for the predator, SIAM J. Appl. Math., 69(2008), 596620.
 Y. Du and Yoshio Yamada, On the longtime limit of positive solutions to the degenerate logistic equation, Discrete and Continuous Dynamical Systems A, 25(2009), 123132.
 F. Cirstea and Y. Du, Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity, J. Functional Anal., 250(2007),317346.
 Y. Du, The heterogeneous AllenCahn equation in a ball: solutions with layers and spikes, J. Diff. Eqns., 244(2008), 117169.
 Y. Du and Kimie Nakashima, Morse index of layered solutions to the heterogeneous AllenCahn equation, J. Diff. Eqns., 238(2007), 87117.
 Y. Du and Xing Liang, A diffusive competition model with a protection zone, J. Diff. Eqns., 244(2008), 6186.
 Y. Du and Junping Shi, Some recent results on diffusive predatorprey models in spatially heterogeneous environment, in Nonlinear Dynamics and Evolution Equations, Eds. Hermann Brunner, XiaoQiang Zhao and Xingfu Zou, Fields Institute Communications Vol. 48, American Math. Soc., 2006, pp 95135.
 Y. Du and Junping Shi, A diffusive predatorprey model with a protection zone, J. Diff. Eqns., 229(2006), 6391.
 F. Cirstea and Y. Du, Large solutions of elliptic equations with a weakly superlinear nonlinearity, J. d'Analyse Math., 103(2007), 261277.
 Y. Du, Z.M. Guo and F. Zhou, Boundary blowup solutions with interior layers and spikes in a bistable problem, Discrete and Continuous Dynamical Systems, 19(2007), 271298.
 Y. Du and Lishan Liu, Remarks on the uniqueness problem of the logistic equation on the entire space, Bull. Australian Math. Soc., 73(2006), 129137.
 Y. Du and Junping Shi, Allee effect and bistability in a spatially heterogeneous predatorprey model, Trans. Amer. Math. Soc., 359(2007), 45574593.
 Y. Du and M.X. Wang, Asymptotic behavior of positive steadystates to a predatorprey model, Proc. Roy. Soc. Edinburgh, 136A(2006), 759778.
 Y. Du and ZM. Guo, The degenerate logistic model and a singularly mixed boundary blowup problem, Discrete and Continuous Dynamical Systems, 14(2006), 129.
 E.N. Dancer and Y. Du, A uniqueness theorem for a free boundary problem, Proc. Amer. Math. Soc., 134(2006), 32233230.
 Y. Du and Z.M. Guo, Boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions, J. Diff. Eqns., 221(2006), 102133.
 F. Cirstea and Y. Du, General uniqueness results and variation speed for blowup solutions of elliptic equations, Proc. London Math. Soc., 91(2005), 459482.
 Y. Du, Bifurcation and related topics in elliptic problems, Handbook for Partial Diff. Eqns.Stationary Partial Differential Equations, Vol. 2, Eds. M. Chipot and P. Quittner, Elsevier, 2005, pp.127209.
 Y. Du and S.J. Li, Nonlinear Liouville theorems and a priori estimates for indefinite superlinear elliptic equations, Adv. Diff. Eqns., 10(2005), 841860.
 Y. Du and X.B. Pan, Multiple states and hysteresis for type I superconductors, J. Math. Physics, 46(2005), 073301(34pp).
 Y. Du, Multiplicity of positive solutions for an indefinite superlinear elliptic problem in R^N, Ann. Inst. Henri Poincare Anal. Non Lineaire, 21(2004), 657672.
 Y. Du and S.B. Hsu, A diffusive predatorprey model in heterogeneous environment, J. Diff. Eqns., 203(2004), 331364.
 Y. Du and Z.M. Guo, Symmetry for elliptic equations in a half space without strong maximum principle, Proc. Roy. Soc. Edinburgh, 134A(2004), 259269.
 Y. Du, Spatial patterns for population models in a heterogeneous environment, (survey article), Taiwanese J. Math., 8(2004), 155182.
 Y. Du and Z.M. Guo, Uniqueness and layer analysis for boundary blowup solutions, J. Math. Pures Appl., 83(2004), 739763.
 Y. Du and S. Yan, Boundary blowup solutions with a spike layer, J. Diff. Eqns., 205(2004), 156184.
 Y. Du, Asymptotic behavior and uniqueness results for boundary blowup solutions, Diff. Integral Eqns., 17(2004), 819834.
Email comments to ydu@turing.une.edu.au