Yihong Du

Publications since 2004:

Books

  1. 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: 981-256-624-4)
  2. Y. Du, Hitoshi Ishii and Wei-Yueh Lin (eds.) Recent Progress in Nonlinear Partial Differential Equations and Viscosity Solutions, World Scientific Publishing, 2009. (372 pages. ISBN: 981-283-473-7)

Papers

  1. Zhiguo Wang, Hua Nie and Y. Du, Spreading speed for a West Nile virus model with free boundary, submitted, 2018.
  2. Y. Du, Bendong Lou, Rui Peng and Maolin Zhou, The Fisher-KPP equation over simple graphs: Varied persistence states in river networks, submitted, 2018. (arXiv:1809.06961)
  3. Y. Du, On the work of Norman Dancer, Disc. Cont. Dyn. Syst-S, 12 (2019), 1807-1833.
  4. 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., to appear ( Published online Feb. 2019)
  5. Y. Du, Fernando Quiros and Maolin Zhou, Logarithmic corrections in Fisher-KPP type porous medium equations, submitted, 2018. (arXiv:1806.02022)
  6. Lei Wei and Y. Du, Positive solutions of elliptic equations with a strong singular potential, Bull. London Math Soc, to appear ( published online Dec 2018).
  7. Weiwei Ding, Y. Du and Zongming Guo, The Stefan problem for the Fisher-KPP equation with unbounded initial range, submitted, 2018.
  8. Shuang Liu, Y. Du and Xinfeng Liu, Numerical methods for a class of reaction-diffusion equations with free boundaries, International J. Computer Math., to appear.
  9. Zhiguo Wang, Hua Nie and Y. Du, Asymptotic spreading speed for the weak competition system with a free boundary, submitted, 2017.(arXiv1710.05485)
  10. 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), 1254-1282. (Published online Feb. 2018).
  11. Y. Du and Messoud Efendiev, Existence and exact multiplicity for quasilinear elliptic equations in quarter-spaces, In: Gurevich P., Hell J., Sandstede B., Scheel A. (eds) "Patterns of Dynamics", pp. 128-137. Springer Proceedings in Mathematics & Statistics, vol 205. Springer, 2016.
  12. Y. Du and Hiroshi Matano, Radial terrace solutions and propagation profile of multistable reaction-diffusion equations over R^N, submitted, 2017.(arXiv 1711.00952)
  13. 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.(arXiv 1710.05482)
  14. 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. (published online July 2017).
  15. 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, to appear.(Published online Jan. 2019)
  16. Weiwei Ding, Y. Du and Xing Liang, Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions, J. Diff. Eqns., 262(2017), 4988-5021. (arXiv1611.01909)
  17. 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), 297-321.
  18. Shangbing Ai, Y. Du and Rui Peng, Traveling waves for a generalized Holling-Tanner predator-prey model, J. Diff. Equations, 263(2017), 7782-7814.
  19. Xuemei Zhang and Y. Du, Sharp conditions for the existence of boundary blow-up solutions to the Monge-Ampere equation, Cal. Var. PDEs, 57:30(2018), 24pages.
  20. 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), 895-911.
  21. 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. (arXiv1505.07689)
  22. 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 (published online Aug. 2017).(arXiv1508.06246)
  23. 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.(arXiv1501.06258)
  24. Y. Du and L. Wei, Boundary behavior of positive solutions to nonlinear elliptic equations with Hardy potential, J. London Math. Soc., 91(2015), 731-749.
  25. L. Wei and Y. Du, Exact singular behavior of positive solutions to nonlinear elliptic equations with a Hardy potential, J. Diff. Eqns., 262(2017), 3864-3886.
  26. Y. Du and Zongming Guo, Finite Morse index solutions of weighted elliptic equations and the critical exponents, Calculus of Variations and PDEs, 54(2015), 3161-3181.
  27. Y. Du, S.B. Hsu and Yuan Lou, Multiple steady-states in phytoplankton population induced by phytoinhibition, J. Diff. Eqns, 258(2015), 2408-2434.
  28. Y. Du, Spreading profile and nonlinear Stefan problems, Bull. Inst. Math. Academia Sinica (Special Issue for Neil Trudinger), 8(2013), 413-430.
  29. 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. (PDF)
  30. P. Alvarez-Caudevilla, Y. Du and Rui Peng, Qualitative analysis of a cooperative reaction-diffusion system in spatiotemporally degenerate environment, SIAM J. Math. Anal., 46(2014), 499-531.
  31. Y. Du, Zongming Guo and Kelei Wang, Monotonicity formula and epsilon-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions, Calculus of Variations and PDEs, 50(2014), 615-638.
  32. 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), 3105-3132. (arXiv1303.0454)
  33. 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. (PDF)
  34. Y. Du, Hiroshi Matano and Kelei Wang, Regularity and asymptotic behavior of nonlinear Stefan problems, Arch. Rational Mech. Anal., 212(2014), 957-1010. (PDF)
  35. 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), 375-396. (PDF)
  36. 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. (PDF)
  37. Y. Du and R. Peng, Sharp spatiotemporal patterns in the diffusive time-periodic logistic equation, J. Diff. Eqns., 254 (2013), 3794-3816.
  38. 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, pp231-238.
  39. Y. Du and Z.M. Guo, Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations, Adv. Diff. Eqns., 18(2013), 737-768. (arXiv1303.4145)
  40. 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), 583-603. (PDF file)
  41. E.N. Dancer, Y. Du and M. Efendiev, Quasilinear elliptic equations on half- and quarter-spaces, Adv. Nonlinear Studies (special issue dedicated to Klaus Schmitt), 13 (2013), 115-136.
  42. Y. Du, Zongming Guo and Rui Peng, A diffusive logistic model with a free boundary in time-periodic environment, J. Funct. Anal., 265 (2013), 2089-2142. (PDF file)
  43. Y. Du and Bendong Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17(2015), 2673-2724. (arXiv1301.5373)
  44. Y. Du and Z.M. Guo, The Stefan problem for the Fisher-KPP equation, J. Diff. Eqns., 253(2012), 996-1035. (PDF file)
  45. Y. Du, Rui Peng and Peter Polacik, The parabolic logistic equation with blow-up initial and boundary values, J. d'Analyse Math., 118 (2012), 297-316.
  46. Y. Du and Linfeng Mei, On a nonlocal reaction-diffusion-advection equation modeling phytoplankton, Nonlinearity, 24(2011), 319-349.
  47. Y. Du and Zongming Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary II, J. Diff. Eqns., 250(2011), 4336-4366. (PDF file)
  48. F. Cirstea and Y. Du, Isolated singularities for weighted quasilinear elliptic equations, J. Functional Anal., 259(2010), 174-202.
  49. Y. Du and Li Ma, A Liouville theorem for conformal Gaussian curvature type equations in $\R^2$, Calculus of Variations and PDEs, 43(2012), 485-505.
  50. Y. Du and Zhigui Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42(2010), 377-405. (PDF file) ERRATUM: SIAM J. Math. Anal., 45(2013), 1995-1996.
  51. Y. Du and S.B. Hsu, On a nonlocal reaction-diffusion problem arising from the modeling of phytoplankton growth, SIAM J. Math. Anal., 42(2010), 1305-1333.
  52. Y. Du and R. Peng, The periodic logistic equation with spatial and temporal degeneracies, Trans. Amer. Math. Soc., 364(2012), 6039-6070. (PDF file)
  53. E.N. Dancer, Y. Du and Zongming Guo, Finite Morse index solutions of an elliptic equation with supercritical exponent, J. Diff. Eqns., 250(2011), 3281-3310.
  54. 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 978-981-283-473-7
  55. Y. Du and Hiroshi Matano, Convergence and sharp thresholds for propagation in nonlinear diffusion problems, J. European Math. Soc., 12(2010), 279-312. (PDF file)
  56. Y. Du, Rui Peng and Mingxin Wang, Effect of a protection zone in the diffusive Leslie predator-prey model, J. Diff. Eqns., 246(2009), 3932-3956.
  57. 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), 137-148.
  58. Y. Du and Z.M. Guo, Positive solutions of an elliptic equation with negative exponent: stability and critical power, J. Diff. Eqns., 246(2009), 2387-2414.
  59. Y. Du and S.-B. Hsu, Concentration phenomena in a nonlocal quasiliear problem modelling phytoplankton I: Existence, SIAM J. Math. Anal. 40(2008), 1419-1440.
  60. Y. Du and S.-B. Hsu, Concentration phenomena in a nonlocal quasiliear problem modelling phytoplankton II: Limiting profile, SIAM J. Math. Anal. 40(2008), 1441-1470.
  61. Y. Du, P.Y.H. Pang and M. Wang, Qualitative analysis of a predator-prey model with stage structure for the predator, SIAM J. Appl. Math., 69(2008), 596-620.
  62. Y. Du and Yoshio Yamada, On the long-time limit of positive solutions to the degenerate logistic equation, Discrete and Continuous Dynamical Systems A, 25(2009), 123-132.
  63. F. Cirstea and Y. Du, Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity, J. Functional Anal., 250(2007),317-346.
  64. Y. Du, The heterogeneous Allen-Cahn equation in a ball: solutions with layers and spikes, J. Diff. Eqns., 244(2008), 117-169.
  65. Y. Du and Kimie Nakashima, Morse index of layered solutions to the heterogeneous Allen-Cahn equation, J. Diff. Eqns., 238(2007), 87-117.
  66. Y. Du and Xing Liang, A diffusive competition model with a protection zone, J. Diff. Eqns., 244(2008), 61-86.
  67. Y. Du and Junping Shi, Some recent results on diffusive predator-prey models in spatially heterogeneous environment, in Nonlinear Dynamics and Evolution Equations, Eds. Hermann Brunner, Xiao-Qiang Zhao and Xingfu Zou, Fields Institute Communications Vol. 48, American Math. Soc., 2006, pp 95-135.
  68. Y. Du and Junping Shi, A diffusive predator-prey model with a protection zone, J. Diff. Eqns., 229(2006), 63-91.
  69. F. Cirstea and Y. Du, Large solutions of elliptic equations with a weakly superlinear nonlinearity, J. d'Analyse Math., 103(2007), 261-277.
  70. Y. Du, Z.M. Guo and F. Zhou, Boundary blow-up solutions with interior layers and spikes in a bistable problem, Discrete and Continuous Dynamical Systems, 19(2007), 271-298.
  71. Y. Du and Lishan Liu, Remarks on the uniqueness problem of the logistic equation on the entire space, Bull. Australian Math. Soc., 73(2006), 129-137.
  72. Y. Du and Junping Shi, Allee effect and bistability in a spatially heterogeneous predator-prey model, Trans. Amer. Math. Soc., 359(2007), 4557-4593.
  73. Y. Du and M.X. Wang, Asymptotic behavior of positive steady-states to a predator-prey model, Proc. Roy. Soc. Edinburgh, 136A(2006), 759-778.
  74. Y. Du and Z-M. Guo, The degenerate logistic model and a singularly mixed boundary blow-up problem, Discrete and Continuous Dynamical Systems, 14(2006), 1-29.
  75. E.N. Dancer and Y. Du, A uniqueness theorem for a free boundary problem, Proc. Amer. Math. Soc., 134(2006), 3223-3230.
  76. 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), 102-133.
  77. F. Cirstea and Y. Du, General uniqueness results and variation speed for blow-up solutions of elliptic equations, Proc. London Math. Soc., 91(2005), 459-482.
  78. 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.127-209.
  79. Y. Du and S.J. Li, Nonlinear Liouville theorems and a priori estimates for indefinite superlinear elliptic equations, Adv. Diff. Eqns., 10(2005), 841-860.
  80. Y. Du and X.B. Pan, Multiple states and hysteresis for type I superconductors, J. Math. Physics, 46(2005), 073301(34pp).
  81. Y. Du, Multiplicity of positive solutions for an indefinite superlinear elliptic problem in R^N, Ann. Inst. Henri Poincare Anal. Non Lineaire, 21(2004), 657-672.
  82. Y. Du and S.B. Hsu, A diffusive predator-prey model in heterogeneous environment, J. Diff. Eqns., 203(2004), 331-364.
  83. Y. Du and Z.M. Guo, Symmetry for elliptic equations in a half space without strong maximum principle, Proc. Roy. Soc. Edinburgh, 134A(2004), 259-269.
  84. Y. Du, Spatial patterns for population models in a heterogeneous environment, (survey article), Taiwanese J. Math., 8(2004), 155-182.
  85. Y. Du and Z.M. Guo, Uniqueness and layer analysis for boundary blow-up solutions, J. Math. Pures Appl., 83(2004), 739-763.
  86. Y. Du and S. Yan, Boundary blow-up solutions with a spike layer, J. Diff. Eqns., 205(2004), 156-184.
  87. Y. Du, Asymptotic behavior and uniqueness results for boundary blow-up solutions, Diff. Integral Eqns., 17(2004), 819-834.



Email comments to ydu@turing.une.edu.au