EN

DATEDecember 31, 2022

**Research Interests****：**

Nonlinear Partial Differential Equations

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**Publications：**

1. Luo Yongbing, Xu Runzhang, Yang Chao, Global well-posedness for a class of semilinear hyperbolic equations with singular potentials on manifolds with conical singularities, Calculus of Variations and Partial Differential Equations, 2022, 61(6), 210.

2. Yang Chao, Radulescu Vicentiu D., Xu Runzhang, Zhang Mingyou, Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models, Advanced Nonlinear Studies, 2022, 22(1), 436-468.

3. Shang Shaoqiang, Continuous Selections of the Set-Valued Metric Generalized Inverse in 2-Strictly Convex Banach Spaces, Acta Mathematica Scientia, 2022, 42(3), 1225-1237.

4. Ge Bin, Lu Jianfang, Multiple solutions for p(x)-curl systems with nonlinear boundary condition, Mathematische Nachrichten, 2022, 295(3), 512-535.

5. Ge Bin, Pucci Patrizia, Quasilinear double phase problems in the whole space via perturbation methods, Advances in Differential Equations, 2022, 27(1-2), 1-30.

6. Jiang Kun, Zhang Xuxi, Event-triggered finite-time adaptive trajectory tracking control for a class of nonlinear non-strict-feedback systems with input saturation and application to a single-link robot, Nonlinear Dynamics, 2022, 10.1007/s11071- 022-07882-w.

7. Wang Guodong, Zuo Bijun, Global existence of weak solutions to the compressible Navier-Stokes equations with temperature-depending viscosity coefficients, SIAM Journal on Mathematical Analysis, 2022, 54(3), 3724-3756.

8. Zhang Xuxi, Wang Xia, Bipartite consensus of multi-agent systems with reduced-order observer-based distributed control protocols, International Journal of Systems Science, 2021, 52(11), 2255-2267.

9. Shang Shaoqiang, Cui Yunan, Approximation and Gateaux differentiability of convex function in Banach spaces, Mathematische Nachrichten, 2021, 294(12), 2413-2424.

10. Li Yanan, Yang Zhijian, Exponential Attractor for the Viscoelastic Wave Model with Time-Dependent Memory Kernels, Journal of Dynamics and Differential Equations, 2021, 10.1007/s10884-021-10035-z.

11. Wang Binsheng, Hou Gangling, Ge Bin, Existence of solutions for double-phase problems by topological degree, Journal of Fixed Point Theory and Applications, 2021, 23(1): 11.

12. Cao Daomin, Wang Guodong, Zuo Bijun, Existence of Steady Symmetric Vortex Patch in a Disk, Journal of Mathematical Fluid Mechanics, 2021, 23(1): 20.

13.Lian Wei, Radulescu Vicentiu D., Xu Runzhang, Yang Yanbing, Zhao Nan, Global well-posedness for a class of fourth-order nonlinear strongly damped wave equations, Advances in Calculus of Variations, 2021, 14(4), 589-611.

14. Robin Ming Chen, Wei Lian, Dehua Wang, Runzhang Xu，A rigidity property for the Novikov equation and the asymptotic stability of peakons, Archive for Rational Mechanics and Analysis, 2021, 241(1), 497-533.

15. Xingchang Wang, Runzhang Xu，Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation, Advances in Nonlinear Analysis, 2021,10:261-288.

16. Jiangbo Han, Runzhang Xu, Yanbing Yang, Asymptotic behavior and finite time blow up for damped fourth order nonlinear evolution equation, Asymptotic Analysis, 2021, 122(3-4): 349-369.

17. Nguyen Huy Tuan,Vo Van Au,Runzhang Xu, Semilinear Caputo time-fractional pseudo-parabolic equations, Communications on Pure & Applied Analysis, 2021, 20(2): 583-621.

18. Ming Chen, Zhilei Liang, Dehua Wang, Runzhang Xu，Energy equality in compressible fluids with physical boundaries，SIAM Journal on Mathematical Analysis, 2020, 52(2)1363-1385.

19. Runzhang Xu, Wei Lian, Yi Niu, Global well-posedness of coupled parabolic systems, Science China Mathematics, 2020, 63, 321-356.

20. Wei Lian, Runzhang Xu, Global well-posedness of nonlinear wave equation with weak and strong damping terms and logarithmic source term, Advances in Nonlinear Analysis, 2020,9(1):613-632.

21. Zhang Xuxi, Liu Xianping, Lewis Frank L., Wang Xia, Bipartite tracking consensus of nonlinear multi-agent systems, Physica A-Statistical Mechanics and its Applications, 2020, 545, 123504.

22. Yuxuan Chen, Runzhang Xu, Global well-posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping, linear strong damping and logarithmic nonlinearity, Nonlinear Analysis, 2020, 192, 111664.

23. Yuxuan Chen, Xiaotong Qiu, Runzhang Xu, Yanbing Yang, Global existence and blowup of solutions for a class of nonlinear wave equations with linear pseudo-differential operator, The European Physical Journal Plus, 2020, 135, 573.

24.Wei Lian, Jihong Shen, Runzhang Xu, Yanbing Yang, Infinite sharp conditions by Nehari manifolds for nonlinear Schrödinger equations, The Journal of Geometric Analysis, 2020,30:1865-1886.

25. Wei Lian, Juan Wang, Runzhang Xu, Global existence and blow up of solutions for pseudo-parabolic equation with singular potential，Journal of Differential Equations，2020,269(6): 4914-4959.

26. Runzhang Xu, Yanbing Yang, Low regularity of solutions to the Rotation- Camassa-Holm type equation with the Coriolis effect, Discrete & Continuous Dynamical Systems, 2020, 40(11): 6507-6527.

27. Li Yanan, Yang Zhijian. Optimal attractors of the Kirchhoff wave model with structural nonlinear damping, Journal of Differential Equations 268 (2020) 7741-7773.

28. Wang Yi, Zuo Bijun, Energy and cross-helicity conservation for the three-dimensional ideal MHD equations in a bounded domain, Journal of Differential Equations, 2020, 268(8), 4079-4101.

29. Nguyen Huy Tuan, Vo Van Au, Runzhang Xu, Renhai Wang, On the initial and terminal value problem for a class of semilinear strongly material damped plate equations, Journal of Mathematical Analysis and Applications, 2020,492(2): 124481.

30. Gebrel Ibrahim E., Wang Ligang, Asokanthan, Samuel F, Dynamic Analysis and Design of a Novel Ring-Based Vibratory Energy Harvester, Vibration, 2019, 2(3), 271-284.

31. Runzhang Xu, Wei Lian, Xiangkun Kong, Yanbing Yang, Fourth order wave equation with nonlinear strain and logarithmic nonlinearity, Applied Numerical Mathematics, 2019, 141, 185–205.

32. Yanbing Yang, Runzhang Xu, Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up, Communications on Pure & Applied Analysis, 2019, 18(3): 1351-1358.

33.Wei Lian, Md Salik Ahmed, Runzhang Xu, Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity，Nonlinear Analysis, 2019,184:239-257.

34. Yongcai Geng, Yachun Li, Dehua Wang, Runzhang Xu, Well-posedness of non-isentropic Euler equations with physical vacuum, Interfaces and Free Boundaries, 2019, 21:231-266.

35. Li Yanan, Yang Zhijian, Da Fang. Robust attractors for a perturbed non-autonomous extensible beam equation with nonlinear nonlocal damping, Discrete and Continuous Dynamical Systems, 2019, 39, 5975-6000.

36. Shaohua Chen, Runzhang Xu, Blow-up of positive solutions to a singular Gierer-Meinhardt system, Nonlinear Analysis: Real World Applications, 2019, 48, 326-336.

37. Runzhang Xu, Qiang Lin, Shaohua Chen, Guojun Wen, Wei Lian, Difficulties in obtaining finite time blowup for fourth-order semilinear Schrodinger equations in the variational method frame, Electron. J. Differential Equations, 2019, No. 83, pp. 1-22.

38. Xingchang Wang, Yuxuan Chen, Yanbing Yang, Jiaheng Li, Runzhang Xu，Kirchhoff-type system with linear weak damping and logarithmic nonlinearities，Nonlinear Analysis, 2019, 188: 475-499.

39. Yang Yanbing, Md Salik Ahmed, Qin Lanlan, Xu Runzhang, Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations, Opuscula Math. 2019, 39, no. 2: 297-313.

40. Ning Pan, Patrizia Pucci, Runzhang Xu, Binlin Zhang, Degenerate Kirchhoff-type wave problems involving the fractional Laplacian with nonlinear damping and source terms, Journal of Evolution Equations, 2019, 19(3), 615-643.

41. Xu Runzhang, Wang Xingchang, Yang Yanbing, Chen Shaohua, Global solutions and finite time blow-up for fourth order nonlinear damped wave equation, Journal of Mathematical Physics, 2018, 56(6):061503.

42. Yanbing Yang，Runzhang Xu，Finite time blowup for nonlinear Klein-Gordon equations with arbitrarily positive initial energy, Applied Mathematics Letters, 2018,77:21-26.

43. Shaohua Chen, Yurij Salmaniw, Runzhang Xu, Global Existence for a Singular Gierer-Meinhardt System, Journal of Differential Equations, 2017, 262, 2940-2960.

44. Runzhang Xu, Mingyou Zhang, Shaohua Chen, Yanbing Yang and Jihong Shen, The initial-boundary value problems for a class of six order nonlinear wave equation, Discrete and Continuous Dynamical Systems, 2017, 37(11)5631-5649.

45. Shaohua Chen, Yurij Salmaniw, Runzhang Xu, Bounded solutions to a singular parabolic system, Journal of Mathematical Analysis and Applications, 2017, 455, 936-978.

46. Xu Runzhang, Yang Yanbing, Initial Value Dependence Problems of Nonlinear Evolution Equations, Science Press, Bei Jing: 2017.

47. S. K. Vishwakarma, Runzhang Xu, G-type dispersion equation under suppressed rigid boundary: analytic approach, Applied Mathematics and Mechanics, 2016, 4, 501-512.

48. Shen Jihong, Zhang Mingyou, Wang Xingchang, Liu Bowei, Xu Runzhang, Global well-posedness for strongly damped multidimensional generalized Boussinesq equations, Mathematical Methods in the Applied Sciences, 2016, 15, 4437-4450.

49. Shaohua Chen, Runzhang Xu, Hongtao Yang, Global and blowup solutions for general Lotka-Volterra system, Communications on Pure and Applied Analysis, 2016, 15, 1757-1768.

50.Xu Runzhang, Yang Yanbing, Liu Bowei, Shen Jihong and Huang Shaobin. Global existence and blowup of solutions for the multidimensional sixth-order “good” Boussinesq equation, Zeitschrift fur angewandte Mathematik und Physik ZAMP, 2015, 66: 955-976.

51. Chen Shaohua and Xu Runzhang. Large time behavior of solutions to degenerate parabolic equations, Nonlinear Differential Equations and Applications NoDEA, 2015, 22: 301-309

52. Xu Runzhang, Wang Xuemei, Niu Yi, Zhang Mingyou and Liu Jie. Sharp criterion of global existence for a class of nonlinear Schrödinger equations with critical exponent, Mathematics and Computers in Simulation, 2015, 107: 46-51.

53. Xu Runzhang, Chen Tianlong, Liu Chunmei and Ding Yunhua. Global well-posedness and global attractor of fourth order semilinear parabolic equation, Mathematical Methods in the Applied Sciences, 2015, 38: 1515-1529.

54. Shang Shaoqiang, Cui Yunan, Uniform nonsquareness and locally uniform nonsquareness in Orlicz-Bochner function spaces and applications, Journal of Functional Analysis, 2014, 267(7), 2056-2076.

55. Xu Runzhang, Su Jia, Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations, Journal Functional Analysis, 2013, 264: 2732-2763.

56. Xu Runzhang, Yang Yanbing, Global existence and asymptotic behaviour of solutions for a class of fourth order strongly damped nonlinear wave equations, Quarterly of Applied Mathematics, 2013,52(3):401-415.

57. Xu Runzhang, Xu Chuang. Sharp conditions of global existence for second-order derivative nonlinear Schrodinger equations with combined power-type nonlinearities, ZAMM- Z. Angew. Math. Mech, 2013,93(1):29-37.

58. Xu Runzhang, Ding Yunhua. Global solutions and finite time blow up for damped Klein-Gordon equation, Acta Matematica Scientia, 2013,33B(3):643-652.

59. Xu Runzhang, Xu Chuang, Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential，Electronic Journal of Differential Equations，2012,2012(211):1-12.

60. Xu Runzhang, Jiang Xiaoli, Liu Jie, Uniform blow-up rate for a compressible reactive gas model, Applied Mathematics and Mechanics (English Edition), 2012,33(1):129-138.

61. Xu Runzhang, Cao Xiuying, Yu Tao, Finite time blow-up and global solutions for a class of semilinear parabolic equations at high energy level, Nonlinear Analysis Series B: Real World Applications,2012, 13(1)197-202.

62. Xu Runzhang, Jin Chunyan, Yu Tao, Liu Yacheng, On quenching for some parabolic problems with combined power-type nonlinearities, Nonlinear Analysis Series B: Real World Applications, 13(2012)333-339.

63. Xu Runzhang, Liu Yacheng, Ill-posedness of nonlinear parabolic equation with critical initial condition, Mathematics and Computers in Simulation 82(2012) 1363-1374.

64. Xu Runzhang, Xu Chuang, Liu Yang, Yu Tao. Well-posedness of nonlinear wave equation with combined power-type nonlinearities, Mathematical Methods in the Applied Sciences, 2011,34(8)869-895.

65. Xu Runzhang, Liu Yacheng, Liu Bowei. The Cauchy problem for a class of multidimensional Boussinesq type equation, Nonlinear Analysis: Theory, Methods & Applications,2011,74(6)2425-2437.

66. Xu Runzhang, Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities, Mathematical Methods in the Applied Sciences, 2011,34(18)2318-2328

67.Xu Runzhang, Initial boundary value problem of semilinear hyperbolic equations and parabolic equations with critical initial data, Quarterly of Applied Mathematics, 2010, LXVIII（3）：459–468.

68. Xu Runzhang, Liu Yacheng, Global existence and blow-up of solutions for generalized Pochhammer-Chree equations, Acta Mathematica Scientia, 2010, 30B(5):1793–1807

69.Runzhang Xu, Yacheng Liu, Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations, Journal of Mathematical Analysis and Applications, 2009,359(2): 739-751.

70. Runzhang Xu, Yacheng Liu, Tao Yu, Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations, Nonlinear Analysis: Theory, Methods & Applications, 2009,71(10) :4977-4983.

71. Liu Yacheng, Xu Runzhang. Potential well method for Cauchy problem of generalized double dispersion equations, Journal of Mathematical Analysis and Applications, 338 (2008) 1169–1187.

72.Liu Yacheng, Xu Runzhang. A class of fourth order wave equations with dissipative and nonlinear strain terms, Journal of Differential Equations, 244 (2008) 200–228.

73. Liu Yacheng, Xu Runzhang. Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation, Physica D: Nonlinear Phenomena, 2008，237：721–731.

74. Liu Yacheng, Xu Runzhang. Potential well method for initial boundary value problem of the generalized double dispersion equations, Communications on Pure and Applied Analysis, 7 (2008), no. 1, 63-81.

75. Liu Yacheng, Xu Runzhang，Yu Tao. Global existence, nonexistence and asymptotic behavior of solutions for Cauchy problem of semilinear heat equations, Nonlinear Analysis-Theory Methods & Applications，2008，68(11)：3332-3348. 2008.6.11

76. Xu Runzhang, Liu Yacheng. Remarks on nonlinear Schrödinger equation with harmonic potential. Journal of Mathematical Physics, 2008, 49(4): 043512-043512-5.

77.Xu Runzhang, Liu Yacheng. Asymptotic behavior of solutions for initial boundary value problem of strongly damped nonlinear wave equations, Nonlinear Analysis Series A: Theory, Methods & Applications, 2008, 69(8): 2492-2495. 2008-10-15.

78. Liu Yacheng, Xu Runzhang, Fourth order wave equations with nonlinear strain and source terms, Journal of Mathematical Analysis and Applications, 331 (2007) 585–607.

**Awards:**

1. Potential Well Family Theory and Its Application to Higher Order Evolution Equations, Heilongjiang Science and Technology Second Prize, 2017

2. Outstanding Youth Academic Award of the First Heilongjiang Provincial, 2016

3. The Dynamic Behavior of Higher Order Evolution Equations and Schrodinger Equations, First Prize of Heilongjiang University Science and Technology Award, 2015

4. Potential well family theory of some nonlinear mathematical physics model equations and parabolic equations, First Prize of Heilongjiang University Science and Technology Award, 2010

5. Global existence, blow up and asymptotic behavior of solutions for nonlinear Klein-Gordon equation with dissipative term，Second prize of Heilongjiang Province Natural Science and Technology Academic Achievement, 2011

6. A class of fourth order wave equations with disspative and nonlinear strain terms，Second prize of Heilongjiang Province Natural Science and Technology Academic Achievement, 2009

**Contact****：**

Xingchang Wang

Email：wangxingchang@hrbeu.edu.cn