Bixiang Wang




Grants

Research Interests

        My research takes on several directions: (1) deterministic and stochastic partial differential equations; (2) infinite-dimensional random dynamical systems; (3) periodic and almost periodic stochastic systems; (4) singular perturbation problems; and (5) mathematical biology.

Publications

  1. Renhai Wang, Lin Shi and Bixiang Wang, Asymptotic behavior of fractional nonclassical diffusion equations driven by nonlinear colored noise on R^N, Nonlinearity.

  2. Renhai Wang and Bixiang Wang, Random dynamics of lattice wave equations driven by infinite-dimensional nonlinear noise, Discrete and Continuous Dynamical Systems, Series B,

  3. Bixiang Wang, Dynamics of fractional stochastic reaction-diffusion equations on unbounded domains driven by nonlinear noise, J. Differential Equations, https://doi.org/10.1016/j.jde.2019.08.007

  4. Dingshi Li, Bixiang Wang and Xiaohu Wang, Random dynamics of fractional stochastic reaction-diffusion equations on R^n without uniqueness, Journal of Mathematical Physics, 60 (2019), 072704, 1-21.

  5. Bixiang Wang, Dynamics of stochastic reaction-diffusion lattice systems driven by nonlinear noise, Journal of Mathematical Analysis and Applications, 477 (2019) 104-132.

  6. Lin Shi, Renhai Wang, Kening Lu and Bixiang Wang, Asymptotic behavior of stochastic FitzHugh-Nagumo systems on unbounded thin domains, Journal of Differential Equations, (267) (2019), 4373-4409.

  7. Jun Shen, Kening Lu and Bixiang Wang, Convergence and center manifolds for differential equations driven by colored noise, Discrete and Continuous Dynamical Systems, Series A, 39 (2019), 4797-4840.

  8. Renhai Wang and Bixiang Wang, Asymptotic behavior of non-autonomous fractional stochastic p-Laplacian equations, Computers and Mathematics with Applications, https://doi.org/10.1016/j.camwa.2019.05.024

  9. Renhai Wang, Yangrong Li and Bixiang Wang, Random dynamics of fractional nonclassical diffusion equations driven by colored noise, Discrete and Continuous Dynamical Systems, Series A, 39 (2019), 4091-4126.

  10. Dingshi Li, Kening Lu, Bixiang Wang and Xiaohu Wang, Limiting dynamics for non-autonomous stochastic retarded reaction-diffusion equations on thin domains, Discrete and Continuous Dynamical Systems, Series A, 39 (2019), 3717-3747.

  11. Bixiang Wang, Weak pullback attractors for stochastic Navier-Stokes equations with nonlinear diffusion terms, Proceedings of the American Mathematical Society, 147 (2019), 1627-1638.

  12. Bixiang Wang, Weak pullback attractors for mean random dynamical systems in Bochner spaces, Journal of Dynamics and Differential Equations, DOI: 10.1007/s10884-018-9696-5

  13. Anhui Gu and Bixiang Wang, Random attractors of FitzHugh-Nagumo systems driven by colored noise on unbounded domains, Stochastics and Dynamics, DOI: 10.1142/S0219493719500357.

  14. Jun Shen, Junyilang Zhao, Kening Lu and Bixiang Wang, The Wong-Zakai approximations of invariant manifolds and foliations for stochastic evolution equations, Journal of Differential Equations, 266 (2019), 4568-4623.

  15. Kening Lu and Bixiang Wang, Wong-Zakai approximations and long term behavior of stochastic partial differential equations, Journal of Dynamics and Differential Equations, DOI: 10.1007/s10884-017-9626-y

  16. Anhui Gu, Kening Lu and Bixiang Wang, Asymptotic behavior of random Navier-Stokes equations driven by Wong-Zakai approximations, Discrete and Continuous Dynamical Systems, Series A, 39 (2019), 185-218

  17. Yadong Shang, Jianjun Paul Tian and Bixiang Wang, Asymptotic behavior of the stochastic Keller-Segel equations, Discrete and Continuous Dynamical Systems, Series B, 24 (2019), 1367-1391.

  18. Hong Lu, Jiangang Qi, Bixiang Wang and Mingji Zhang, Random attractors for non-autonomous fractional stochastic parabolic equations on unbounded domains, Discrete and Continuous Dynamical Systems, Series A, 39 (2019), 683-706.

  19. Anhui Gu, Dingshi Li, Bixiang Wang and Han Yang, Regularity of random attractors for fractional stochastic reaction-diffusion equations on R^n, Journal of Differential Equations, 264 (2018), 7094-7137.

  20. Anhui Gu and Bixiang Wang, Asymptotic behavior of random FitzHugh-Nagumo systems driven by colored noise, Discrete and Continuous Dynamical Systems Series B, 23 (2018), 1689-1720.

  21. Xiaohu Wang, Kening Lu and Bixiang Wang, Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains, Journal of Differential Equations, 264 (2018), 378-424.

  22. Dingshi Li, Kening Lu, Bixiang Wang and Xiaohu Wang, Limiting behavior of dynamics for stochastic reaction-diffusion equations with additive noise on thin domains, Discrete and Continuous Dynamical Systems, Series A, 38 (2018), 187-208.

  23. Bixiang Wang, Asymptotic behavior of non-autonomous fractional stochastic reaction-diffusion equations, Nonlinear Analysis TMA, 158 (2017), 60-82.

  24. Bixiang Wang, Multivalued non-autonomous random dynamical systems for wave equations without uniqueness, Discrete and Continuous Dynamical Systems, Series B, 22 (2017), 2011-2051. arXiv:1507.02013.

  25. Dingshi Li, Bixiang Wang and Xiaohu Wang, Limiting behavior of non-autonomous stochastic reaction-diffusion equations on thin domains, Journal of Differential Equations, 262 (2017), 1575-1602.

  26. Xiaohu Wang, Kening Lu and Bixiang Wang, Exponential stability of non-autonomous stochastic delay lattice systems with multiplicative noise, Journal of Dynamics and Differential Equations, 28 (2016), 1309-1335

  27. Bixiang Wang, Periodic and almost periodic random inertial manifolds for non-autonomous stochastic equations, 189-208, Continuous and Distributed Systems II: Theory and Applications, Edited by V.A. Sadovnichiy and M.Z. Zgurovsky, Springer, 2015, arXiv:1409.3883.

  28. Xiaohu Wang, Kening Lu and Bixiang Wang, Long term behavior of delay parabolic equations with additive noise and deterministic time dependent forcing, SIAM Journal on Applied Dynamical Systems, 14 (2015), 1018-1047.

  29. Bixiang Wang, Stochastic bifurcation of pathwise random almost periodic and almost automorphic solutions for random dynamical systems, Discrete and Continuous Dynamical Systems, 35 (2015), 3745-3769.

  30. Bixiang Wang, Existence, stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations, Nonlinear Analysis TMA, 103 (2014), 9-25.

  31. Peter W. Bates, Kening Lu and Bixiang Wang, Attractors of non-autonomous stochastic lattice systems in weighted spaces, Physica D, 289 (2014), 32-50.

  32. Bixiang Wang, Existence and upper semicontinuity of attractors for stochastic equations with deterministic non-autonomous terms, Stochastics and Dynamics, 14 (2014), No. 4, 1450009, 1-31.

  33. Andrew Krause and Bixiang Wang, Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains, J. Math. Anal. Appl., 417 (2014), 1018-1038.

  34. Bixiang Wang, Random attractors for non-autonomous stochastic wave equations with multiplicative noise, Continuous and Discrete Dynamical Systems, 34 (2014), 269-300.

  35. Andrew Krause, Michael Lewis and Bixiang Wang, Dynamics of the non-autonomous stochastic $p$-Laplace equation driven by multiplicative noise, Applied Mathematics and Computation, 246 (2014), 365-376.

  36. Bixiang Wang and Boling Guo, Asymptotic behavior of non-autonomous stochastic parabolic equations with nonlinear Laplacian principal part, Electronic J. Differential Equations, 2013 (2013), No. 191, 1-25.

  37. Abiti Adili and Bixiang Wang, Random attractors for non-autonomous stochastic FitzHugh-Nagumo systems with multiplicative noise, Continuous and Discrete Dynamical Systems, Supplement (2013), 1-10.

  38. Peter W. Bates, Kening Lu and Bixiang Wang, Tempered random attractors for parabolic equations in weighted spaces, J. Math. Physics, 54 (2013), 081505, 1-26.

  39. Robert Jones and Bixiang Wang, Asymptotic behavior of a class of stochastic nonlinear wave equations with dispersive and dissipative terms, Nonlinear Analysis, Real World Applications, 14 (2013), 1308-1322.

  40. Abiti Adili and Bixiang Wang, Random attractors for stochastic FitzHugh-Nagumo systems driven by deterministic non-autonomous forcing, Continuous and Discrete Dynamical Systems Series B, 18 (2013), 643-666.

  41. Bixiang Wang, Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems, J. Differential Equations, 253 (2012), 1544-1583.

  42. Bixiang Wang, Periodic random attractors for stochastic Navier-Stokes equations on unbounded domains, Electronic J. Differential Equations, 2012 (2012), No. 59, 1-18.

  43. Bixiang Wang, Asymptotic behavior of stochastic wave equations with critical exponents on R^3, Transactions of AMS, 363 (2011), 3639-3663.

  44. Bixiang Wang, Almost periodic dynamics of perturbed infinite-dimensional dynamical systems, Nonlinear Analysis TMA, 74 (2011), 7252-7260.

  45. Weishi Liu and Bixiang Wang, Poisson-Nernst-Planck systems for narrow tubular-like membrane channels, J. Dynamics and Differential Equations, 22 (2010), 413-437.

  46. Kasimir Gabert and Bixiang Wang, Non-autonomous attractors for singularly perturbed parabolic equations on R^n, Nonlinear Analysis TMA, 73 (2010), 3336-3347.

  47. Bixiang Wang and Robert Jones, Asymptotic behavior of a class of non-autonomous degenerate parabolic equations, Nonlinear Analysis TMA, 72 (2010) 3887-3902.

  48. Bixiang Wang and Xiaoling Gao, Random attractors for wave equations on unbounded domains, Discrete and Continuous Dynamical Systems, Special (2009), 800-809.

  49. Bixiang Wang, Upper semicontinuity of random attractors for non-compact random dynamical systems, Electronic J. Differential Equations, 2009 (2009), No. 139, 1-18.

  50. Bixiang Wang, Random attractors for the stochastic FitzHugh-Nagumo system on unbounded domains, Nonlinear Analysis TMA, 71 (2009), 2811-2828.

  51. Bixiang Wang, Pullback attractors for the non-autonomous FitzHugh-Nagumo system on unbounded domains, Nonlinear Analysis TMA, 70 (2009), 3799-3815.

  52. Bixiang Wang, Random attractors for the stochastic Benjamin-Bona-Mahony equation on unbounded domains, J. Differential Equations, 246 (2009), 2506-2537.

  53. Bixiang Wang, Pullback attractors for non-autonomous Reaction-Diffusion equations on R^n, Frontiers of Mathematics in China, 4 (2009), 563-583.

  54. Bixiang Wang, Long time behavior of lattice Schrodinger systems, Advances in Mathematics Research, 9 (2009), 1-19.

  55. Peter W. Bates, Kening Lu and Bixiang Wang, Random attractors for stochastic Reaction-Diffusion equations on unbounded domains, Journal of Differential Equations, 246 (2009), 845-869.

  56. Guglielmo Fucci, Bixiang Wang and Preeti Singh, Asymptotic behavior of the Newton-Boussinesq equation in a two-dimensional channel, Nonlinear Analysis, 70 (2009), 2000-2013.

  57. Bixiang Wang and Siyu Lin, Existence of global attractors for the three-dimensional Brinkman-Forchheimer equation, Mathematical Methods in the Applied Sciences, 31 (2008), 1479-1495.

  58. Bixiang Wang, Uniform attractors of non-autonomous discrete Reaction-Diffusion systems in weighted spaces, Internat. J. Bifur. Chaos, 18 (2008), 695-716.

  59. Timothy Trujillo, Bixiang Wang, Continuity of strong solutions of the Reaction-Diffusion equation in initial data, Nonlinear Analysis, 69 (2008), 2525-2532.

  60. Bixiang Wang, Daniel W. Fussner, Chenggeng Bi, Existence of global attractors for the Benjamin-Bona-Mahony equation in unbounded domains, J. Phys. A, 40 (2007), 10491-10504.

  61. Bixiang Wang, Dynamical behavior of the almost-periodic discrete FitzHugh-Nagumo systems, Internat. J. Bifur. Chaos, 17 (2007), 1673-1685.

  62. Bixiang Wang, Asymptotic behavior of non-autonomous lattice systems, J. Math. Anal. Appl., 331 (2007), 121-136.

  63. Weishi Liu, Bixiang Wang, Asymptotic behavior of the FitzHugh-Nagumo system, Internat. J. of Evolution Equations, 2 (2007), 129-163.

  64. Bixiang Wang, Dynamics of systems on infinite lattices, J. Differential Equations, 221 (2006), 224-245.

  65. Milena Stanislavova, Atanas Stefanov, Bixiang Wang, Asymptotic smoothing and attractors for the generalized Benjamin-Bona-Mahony equation on R^3 , J. Differential Equations, 219 (2005), 451-483.

  66. Erik Van Vleck, Bixiang Wang, Attractors for lattice FitzHugh-Nagumo systems, Physica D, 212 (2005), 317-336.

  67. Kening Lu, Bixiang Wang, Upper semicontinuity of attractors for the Klein-Gordon-Schrodinger equation on unbounded domains, Internat. J. Bifur. Chaos, 15 (2005), 157-168.

  68. Christopher Kumar Anand, Tamas Terlaky, Bixiang Wang, Rapid and embeddable design method for magnetic resonance image reconstruction resampling kernels, Optimization and Engineering, 5 (2004), 485-502.

  69. Bixiang Wang, Uniqueness of solutions for the Ginzburg-Landau model of superconductivity in three spatial dimensions, J. Math. Anal. Appl. 266 (2002), 1-20.

  70. Peter W. Bates, Kening Lu, Bixiang Wang, Attractors for lattice dynamical systems, International J. of Bifurcation and Chaos, 11 (2001), 143-153.

  71. Kening Lu, Bixiang Wang, Attractors for Klein-Gordon-Schrodinger equation in unbounded domains, J. Differential Equations, 170 (2001), 281-316.

  72. Wanli Yang, Bixiang Wang, On the question of global existence for the two-component reaction diffusion systems with the mixed boundary conditions, Nonl. Anal. TMA, 39 (2000), 755-766.

  73. Bixiang Wang, Attractors for reaction diffusion equations in unbounded domains, Physica D, 128 (1999), 41-52.

  74. Bixiang Wang, Existence of time periodic solutions for the Ginzburg-Landau equations of superconductivity, J. Math. Anal. Appl., 232 (1999), 394-412.

  75. Bixiang Wang, Ning Su, Weak solutions of Ginzburg-Landau equations of superconductivity, Appl. Math. Lett., 12 (1999), No. 3, 115-118.

  76. Bixiang Wang, Horst Lange, Attractors for the Klein-Gordon-Schrodinger equation, J. Math. Phys., 40 (1999), 2445-2457.

  77. Bixiang Wang, Ning Su, Existence of solutions for Ginzburg-Landau equations of superconductivity in three spatial dimensions, Proceedings of Royal Society of Edinburgh, 129A (1999), 627-639.

  78. Anibal Rodriguez-Bernal, Bixiang Wang, Robert Willie, Asymptotic behaviour of time-dependent Ginzburg-Landau equations of superconductivity, Math. Methods in Appl. Sciences, 22 (1999), 1647-1669.

  79. Anibal Rodriguez-Bernal, Bixiang Wang, Attractors for partly dissipative reaction diffusion equations, J. Math. Anal. Appl., 252 (2000), 790-803.

  80. Horst Lange, Bixiang Wang, Regularity of attractors for the Klein-Gordon-Schrodinger equation, Math. Methods in Appl. Sciences, 22 (1999), 1535-1554.

  81. Anibal Rodriguez-Bernal, Bixiang Wang, Reduction of dimensions of approximate inertial manifolds by symmetry, Bull. Australian Math. Soc., 60 (1999), 319-330.

  82. Anibal Rodriguez-Bernal, Bixiang Wang, Cauchy problem for the time dependent Ginzburg-Landau model of superconductivity, Proceedings of Royal Society of Edinburgh 130A (2000), 1383-1404.

  83. Boling Guo, Bixiang Wang, Finite dimensional behaviour for the derivative Ginzburg-Landau equation in two spatial dimensions, Physica D, 89(1995), 83-99.

  84. Bixiang Wang, Boling Guo, Attractors for the Davey-Stewartson system on R^2, J. Math. Physics, 38(1997), 2524-2534.

  85. Bixiang Wang, Wanli Yang, Finite dimensional behaviour for the Benjamin-Bona-Mahony equation, J. Phys. A, 30(1997), 4877-4885.

  86. Bixiang Wang, Strong attractors for the Benjamin-Bona-Mahony equation, Appl. Math. Lett., 10(1997), 23-28.

  87. Bixiang Wang, Attractors and approximate inertial manifolds for the generalized Benjamin-Bona-Mahony equation, Math. Methods in Appl. Sciences, 20(1997), 189-203.

  88. Hans G. Kaper, Bixiang Wang, Shouhong Wang, Determining nodes for the time dependent Ginzburg-Landau equations of superconductivity, Discrete and Continuous Dynamical Systems, 4(1998), 205-224.

  89. Bixiang Wang, Regularity of attractors for the Benjamin-Bona-Mahoney equation, J. Phys. A, 31 (1998), 7635-7645.

  90. Bixiang Wang, Shouhong Wang, Gevrey class regularity for the time dependent Ginzburg-Landau equations of superconductivity, Discrete and Continuous Dynamical Systems , 4 (1998), 507-522.

  91. Boling Guo, Bixiang Wang, Gevrey class regularity and approximate inertial manifolds for the Newton-Boussinesq equation, Chinese Annals of Math., 19B (1998), 179-188.

  92. Boling Guo, Bixiang Wang, Gevrey regularity and approximate inertial manifolds for the derivative Ginzburg-Landau equation in two spatial dimensions, Discrete and Continuous Dynamical Systems, 2(1996), 455-466.

  93. Xianling Fan, Bixiang Wang, Remarks on periodic solutions of prescribed energy for singular Hamiltonian systems, Houston J. Math., 17(1991), 385-393.

  94. Boling Guo, Bixiang Wang, Global existence theory for the two dimensional derivative Ginzburg-Landau equation, Chinese Sci. Bull. 43 (1998), 393--395.

  95. Boling Guo, Bixiang Wang, Exponential attractors for the generalized Ginzburg-Landau equation, Acta Math. Sin., 16 (2000), 515--526.

  96. Boling Guo, Bixiang Wang, Weak solutions to the two dimensional derivative Ginzburg-Landau equation, Acta Math. Appl. Sinica, 15 (1999),1-8.

  97. Boling Guo, Bixiang Wang, Attractors for the long-short wave equations, J. Partial Diff. Equations, 11 (1998), 361--383.

  98. Boling Guo, Bixiang Wang, Upper semicontinuity of attractors for the reaction diffusion equation, Acta Math. Scientia, 18 (1998), 139-145.

  99. Boling Guo, Bixiang Wang, Global existence for the Landau-Lifshitz equation, Acta Math. Scientia, 17 (1997), 429-436.

  100. Bixiang Wang, Ke Shi, On nonlinear Galerkin approximation, J. Computational Math., 17(1997), 23-35.

  101. Boling Guo, Bixiang Wang, Approximate inertial manifolds for the Newton-Boussinesq equation, J. Partial Diff. Equ., 9(1996), 237-250.

  102. Boling Guo, Bixiang Wang, The global solution and its long time behaviour for a class of generalized LS type equations, Progress in Natural Science, 6(1996), 533-546.

  103. Boling Guo, Bixiang Wang, Approximation to the global attractor of nonlinear Schrodinger equation, Appl. Math. , J. Chinese Univ., 11(1996), 125-136.

  104. Xianling Fan, Bixiang Wang, Error analysis of nonlinear Galerkin methods for Kuramoto-Sivashinsky equations, Numer. Math. J. Chinese Univ. 5 (1996), 49-61.

  105. Xianling Fan, Bixiang Wang, Conservative periodic solutions of prescribed average energy for singular Hamiltonian inclusions, J. Math. Study, 28(1995), 1-10.

  106. Boling Guo, Bixiang Wang, The global solution and its long time behaviour for a class of generalized LS type equations, Advances in Math.(China), 24(1995), 179-181.

  107. Boling Guo, Bixiang Wang, Approximation to the global attractor of for the Landau-Lifshitz equation of the Ferromagnetic spin chain, Beijing Math., 1(1995), 164-174.

Publications Listed in Mathematical Reviews