Montreal Olympics Stadium


Full List of  Research Papers:

My research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)Fonds de recherche du Quebec Nature et technologies (FRQNT) , and Fédération de  cégeps (the former name: Cegeps International).  

     NSERC fundings
      1. ``Non-monotone traveling waves for reaction-diffusion equations with delay", NSERC Individual Discovery Grant 354724-2016,    years: 2016-2021.      $18,000/year,   in total $90,000  
      2.   ``Damped Euler-Poisson equations and nonlinear diffusion waves", NSERC Individual Discovery Grant 354724-2011,   years: 2011-2016.          $10,000/year, in total $50,000    
      3.  ``Phase transitions and partial differential equations of mixed type", NSERC Individual Discovery Grant 354724-2008,    years: 2008-2011.  $14,000/year, in total $42,000

     FRQNT fundings:
      4.  ``Euler-Poisson équations de modèles semi-conducteurs avec limite sonique " FRQNT grant 256440,  years 2018-2021.          $32,000/year, in total $96,000
      5. ``Stabilitédes ondes oscillatoires de déplacement pour les équations de réaction-diffusion à retardement ",  FRQNT grant 192571, years: 2015-2018.         $36,000/year, in total $108,000
      6. ``Études des équations d'évolution non linéaires de la dynamique des fluides", FRQNT grant 164832,    years: 2012-2015.       $28,000/year, in total $84,000
  
 
     CEGEP International
      7. ``Collaboration internationale de la recherche scientifique à Beijing ", Fédération de  cégeps, year: 2014-2015.      $3,000
      8. ``Collaboration internationale de la recherche scientifique à Italie ", CEGEP International,   year: 2013-2014.    $3,000
      9. ``Collaboration internationale de la recherche scientifique à Hong Kong et au Japon ", CEGEP International,   year: 2012-2013.   $3,000

I also serve as the editorial board for some SCI journals:
Here is a full list of my publication. At least 4 papers are the most cited papers in the top 1% of the world for mathematics  in this decade by ESI (see 2018 Clarivate, Web of Science).. For reviews of my publications in Mathematical Reviews, look here. For citations of my publication, please look at Google Scholar.


A. Preprints / Submitted Papers

[90].  Stability of steady-states for 3-D hydrodynamic model of unipolar semiconductor with Omega contact boundary in hollow ball (with Xiaochun Wu, and Yongqian Zhang), in preparation

[89].  Propagating properties of a chemotaxis model with degenerate diffusion: initial shrinking, eventual smoothness and expanding (with Tianyuan Xu, Shanming Ji, and Jingxue Yin),  submitted.

[88].  Global Solution for Gas-Liquid Flow of 1-D van der Waals Equation of State with Large Initial Data (with Qiaolin He, Xiaoding Shi, and Xiaoping Wang), submitted.

[87].
Global stability of traveling waves with oscillations for time-delayed nonlocal dispersion equations (with Tianyuan Xu, Shanming Ji, and Jingxue Yin),  submitted.

[86].  Asymptotic behavior of solutions to  bipolar Euler-Poisson equations with time-dependent damping (with Haitong Li, Jingyu Li, and Kaijun Zhang), submitted..


[85].  Convergence to rarefaction waves  for Cauchy problem to damped wave equations with time-gradually-degenerate diffusion (with Lili Fan, and Bruno Rubino),  in preparation.

[84].  
Large-time behavior of solutions for Cauchy problem to damped wave equations with time-gradually-degenerate diffusion (with Lili Fan, and Bruno Rubino),  in preparation.
 


B. Accepted / Published Papers (all papers can be downloaded by clicking [PDF] at the end of each item)

[83].  Tianyuan Xu, Shanming JiChunhua JinM. Mei,  and Jingxue YinEarly and late stage profiles for a new chemotaxis model with density-dependent jump probability and quorum-sensing mechanisms, Math. Biosci.  Engin. Vol. 15, No. 6 (2018) 1345--1385.  [PDF]   

[82].  M. MeiKaijun Zhang and Qifeng Zhang,  Global stability of critical traveling waves with oscillations for time-delayed reaction-diffusion equationInt. J. Numer. Anal. Model.,  15 (2019), in press.  [PDF in arXiv]

[81].  Tianyuan Xu, Shanming JiM. Mei, and Jingxue Yin, Traveling waves for time-delayed reaction diffusion equations with degenerate diffusion,  J. Differential Equations, 265 (2018), 4442-4485.  [PDF]

[80].  Yazhou Chen, Qiaolin He, M. Mei and Xiaoding Shi, Asymptotic Stability of Solutions for 1-D Compressible Navier-Stokes-Cahn-Hilliard system ,  J. Math. Anal. Appl., 467 (2018), 185-206. [PDF]     [PDF in arXiv]

[79] Tianyuan Xu, Shanming Ji,
M. Mei and  Jingxue Yin, Global existence of solutions to a chemotaxis-haptotaxis model with density-dependent jump probability and quorum-sensing mechanisms, Math. Methods Appl. Sci. Vol. 41,   (2018), 4208--4226. [PDF].  https://doi.org/10.1002/mma.4883
 
[78]  Rui Huang, Chunhua Jin,  M. Mei and  Jingxue Yin,  Existence and stability of traveling waves for degenerate reaction-diffusion equation with time delay,  J. Nonlinear Science,   Vol. 28,   (2018), 1011-1042.  [PDF].  https://doi.org/10.1007/s00332-017-9439-5

[77].
 J. Li, G. ZhangM. Mei i and K. Zhang, Steady hydrodynamic model of semiconductors with sonic boundary: (II) Supersonic doping profile,  SIAM J. Math. Anal.  Vol. 50, No. 1,  (2018),  718--734.  [PDF]  

[76]
.  J. Li, G. ZhangM. Mei i and K. Zhang, Steady hydrodynamic model of semiconductors with sonic boundary: (I) Subsonic doping profile,  SIAM J. Math. Anal.  Vol. 49, No. 6, (2017), pp. 4767--4811 [PDF]  

[75].  
Haitong Li, Jingyu LiM. Mei and Kaijun Zhang, Convergence to nonlinear diffusion waves for solutions of p-system with time-dependent damping,   J. Math. Anal. Appl.,   456 (2017)  849--871. [PDF].

[74]
. F. Di Michele, M. Mei, B. Rubino and R. Sampalmieri, Thermal equilibrium solution to bipolar hybrid quantum hydrodynamical model, ,J. Differential Equations,  263 (2017)  1843--1873.  [PDF]

[73]. H. Hu, M. Mei, and K. Zhang, Relaxation limit in the bipolar semiconductor hydrodynamic model with non-constant doping profile,  J. Math. Anal. Appl.,  448 (2017) 1175--1203.  [PDF],

[72]. Q. Zhang,  M. Mei, and C.-J. Zhang, Higher-order linearized multistep finite difference methods for non-Fickian delay reaction-diffusion equations, Int. J. Numer. Anal. Model.,  14 (2017) 1--19. [PDF]

[71].  F. Di Michele, M. Mei,  B. Rubino and R. Sampalmieri, Stationary solutions to hybrid quantum hydrodynamical model of semiconductors in bounded domain,  Int. J. Numer. Anal. Model..Vol. 13 No. 6, (2016),  898--925. [PDE]

[70]. Haifeng HuM. Mei, and Kaijun Zhang,  Asymptotic analysis on a bipolar quantum semiconductor hydrodynamic model, Commun. Math. Sci., Vol. 14, No. 8 (2016), pp. 2331-2371. [PDF]

[69] Yuanxiao Li,  M. Mei, and Kaijun Zhang,  Existence of multiple nontrivial solutions for a p-Kirchhoff type elliptic problem involving sign-changing weight functions, Discrete Contin. Dyn. Syst. -- Series B, 21 (2016), 883--908. [PDF]

[68]. Z.-X. Yu and M. Mei,  Uniqueness and stability of traveling waves for cellular neural networks with multiple delays, J. Differential Equations,  260 (2016) , 241--267. [PDF] [Most cited paper]

[67].  Rui Huang, M. Mei,  Kaijun Zhang and Q. Zhang, Asymptotic stability of non-monotone traveling waves  for time-delayed nonlocal dispersion equations,   Discrete Contin. Dyn. Syst. -- Series A, 38 (2016) 1331--1353. [PDF]

[66]. M. Mei,  Hongyu Peng and Zhi-An Wang, Asymptotic profile of a parabolic-hyperbolic system with boundary effect arising from tumor angiogenesis, J. Differential Equations,  259 (2015), 5168--5191. [PDF]

[65].  I-L. Chern, M. Mei,  Xiongfeng Yang, and Q. Zhang, Stability of  non-montone critical traveling waves for reaction-diffusion equations with time-delay, J. Differential Equations,  259 (2015), 1503--1541. [PDF] [Most cited paper]

[64].  Rui HuangM. Mei and  Jingxue Yin, Classical solutions for the Cahn-Hilliard equation with decayed mobility,  Bound. Value Probl. 2014, 2014:264. [PDF]

[63].  C.-K. Lin, C.-T. Lin, Y. Lin,  and M. Mei, Exponential Stability of Nonmonotone Traveling Waves for Nicholson's Blowflies Equation,     SIAM J. Math. Anal.  Vol. 46 (2014), pp. 1053-1084. [PDF] [Most cited paper]

[62]. D. Donatelli, M. Mei B. Rubino, and R. Sampalmieri, Asymptotic behavior of solutions to the Cauchy prolem of Euler-Poisson equations, J. Differential Equations, Vol. 255, No. 10, (2013), 3150--3184. [PDF]

[61]Z.-X. Yu, M. Mei,  Asymptotics and uniqueness of travelling waves for non-monotone delayed systems on 2D lattices, Canadian Math. Bulletin,  56 (2013), 659--672. [PDF]

[60]M. Mei, B. Rubino, and R. Sampalmieri Asymptotic behavior of solutions to the bipolar  hydrodynamic model of semiconductors in bounded domain, Kinetics and Related Models, Vol. 5, No. 3 (2012), 537--550.  [PDF]

[59]. F.-M. Huang, M. Mei, Y. Wang, and T. Yang, Long-time behavior of solutions for bipolar hydrodynamic model of semiconductors with boundary effects, SIAM J. Math. Anal., Vol. 44,  (2012), 1134--1164. [PDF]

[58].  Rui Huang, M. Mei, Y. Wang, Planar traveling waves for nonlocal dispersion equation with monostable nonlinearity,  Discrete Contin. Dyn. Syst. -- Series A, Vol. 32, (2012), 3621--3649.  [PDF]. 

[57]. M. Mei, Y. Wang, Stability of  stationary waves for full Euler-Poisson system  in multi-dimensional space, Commun. Pure Appl. Anal. 11 (2012), 1775--1807.  [PDF]

[56]. M. Mei, Y. Wang, Remark on stability of traveling waves for nonlocal Fisher-KPP equations,  International Journal of Numerical Analysis and Modeling, Series  B, Vol.2, No.4, (2011), 379-401. [PDF]

[55]. F.-M. Huang, M. Mei, Y. Wang, Large-time behavior of solutions to n-dimensional bipolar hydrodynamical model of semiconductors, SIAM J. Math. Anal., Vol. 43, No.4, (2011),.1595--1630. [PDF]

[54]. F.-M. Huang, M. Mei, Y. Wang and H. Yu,  Asymptotic convergence to planar stationary waves for multi-dimensional unipolar hydrodynamic model of semiconductors,  J. Differential Equations, 251 (2011), 1305–1331. [PDF]

[53]. F.-M. Huang, M. Mei, Y. Wang and H. Yu, Asymptotic convergence to stationary waves for unipolar hydrodynamic model of semiconductors, SIAM J. Math. Anal., Vol. 43, No.1, (2011), 411-429. [PDF]

[52]. M. Mei, C.H. Ou and X.-Q. Zhao, Global stability of monostable traveling waves for  nonlocal time-delayed reaction-diffusion equations,  SIAM J. Math. Anal., Vol. 42, No.6 (2010), 2762--2790. [PDF],   Vol. 44, No.1 (2012), pp 538--540. [Erratum]

[51]. M. Mei, Best asymptotic profile for hyperbolic p-system with damping, SIAM J. Math. Anal., Vol. 42, No.1 (2010), 1-23. [PDF]

[50]. H. Ma, M. Mei, Best asymptotic profile for linear damped p-system with boundary effect,  J. Differential Equations, 249 (2010), 446--484.  [PDF]

[49] C.-K. Lin, C-T. Lin, M. Mei, Asymptotic Behavior of Solution to Nonlinear Damped p-System with Boundary Effect, International Journal of Numerical Analysis and Modeling, Series  B, 1 (2010).  [PDF]

[48]. C.-K. Lin, M. Mei,  On travelling wavefronts of the Nicholson's blowflies equation with diffusion,   Proc. Royal Soc. Edinburgh (A), 140A (2010), 135--152. [PDF]

[47]. D. Wei,   J. Y. Wu, M. Mei, Remark on critical speed of traveling wavefronts for Nicholson's blowflies equation with diffusion,  Acta Math. Sci., 30B (5),  (2010) . [PDF]

[46]. M. Mei,  Hyperbolic damped p-system and diffusion phenomena, a survey paper appeared in the RIMS lecture series of "Mathematical Analysis in Fluid and Gas Dynamics", RIMS Kôkyûroku,  Kyoto University, Japan, 2010. [PDF]

[45].Nonlinear diffusion waves for hyperbolic p-system with nonlinear damping ,  J.  Differential Equations, 247 (2009), 1275--1269. [PDF]

[44].. Traveling wavefronts for time-delayed reaction-diffusion equation: (I) local nonlinearity (with  C.-K. Lin, C-T. Lin, and J.W.-H. So),  J. Differential Equations247 (2009), 495--510.  [PDF] [Most cited paper]

[43].Traveling wavefronts for time-delayed reaction-diffusion equation: (II) nonlocal nonlinearity (with  C.-K. Lin, C-T. Lin, and J.W.-H. So),  J. Differential Equations, 247 (2009), 511--529.  [PDF]

[42].. Novel stability results for travelling wavefronts in an age-structured reaction-diffusion population model (with Y. S. Wong),  Math. Biosci. Engin., (2009), 743--752. [PDF]

[41]. M. Mei, Stability of Traveling Wavefronts for Time-Delayed Reaction-Diffusion Equations, Proceedings of the 7th AIMS International Conference ( Texas, USA), Discrete Cont. Dyn. Syst., Supplement 2009, 526--535. [PDF]

[40]. M. Mei, J.W.-H. So Stability of strong traveling waves for a non-local time-delayed reaction-diffusion equation, Proc. Royal Soc. Edinburgh (A). 138 (2008), 551--568. [PDF]

[39]. D. Wei, J.-Y. Wu, M. Mei, A more effective iteration method for solving algebraic equations ,   Applied Mathematical Sciences, 2 (2008), no. 28, 1387--1391.  [PDF]

[38]. L.-P. Liu, M. Mei, and Y. S. Wong, Stationary solutions of phase transition in a coupled viscoelastic system, ``Nonlinear Analysis Research Trends'', Edited by N. Roux, Nova Science Publishers, Inc. 2008, p.p. 277--293. [PDF]

[37]. G. LiM. Mei, and Y. S. Wong, Nonlinear stability of travelling wavefronts in an age-structured reaction-diffusion population model, Mathematical Biosciences and Engineerings, 5, No. 1, (2008),  85--100. [PDF]

[36]. J.-Y. Wu, D. Wei, M. Mei, Analysis on the critical speed of traveling waves, Applied Math. Letters, 20 (2007) 712--718. [PDF]

[35]. M. Gander, M. Mei,  and G. Schmidt, Phase transition for a relaxation model of mixed type with periodic boundary condition, Applied Mathematics Research eXpress, Vol. 2007, Article ID: abm006, Oxford University Press, p.p. 1-34, 2007. [PDF]

[34]. L.-P. Liu, M. Mei, and Y. S. Wong, Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) existence and uniform boundedness , Discrete Cont. Dyn. Syst.,-- B, 7 (2007) 825--837. [PDF]

[33]. L.-P. Liu, M. Mei, and Y. S. Wong, Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (II) convergence , Discrete Cont. Dyn. Syst.,-- B, 7 (2007) 839--857. [PDF]

[32]. L.-P. Liu, M. Mei, and Y. S. Wong, Asymptotic behavior of solutions to the Rosenau-Burgers equation with a periodic initial boundary, Nonlinear Analysis, 65 (2007) 2527--2539. [PDF]

[31]. P. Marcati,  M. Mei, and B. Rubino, Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping, J. Math. Fluid Mech. 7 (2005). [PDF]

[30]. M. Mei, J.W.-H. So, M. Li and S.S. Shen, Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion, Proc. Royal Soc. Edinburgh, 134A (2004) 579--594. [PDF]

[29] L.-P. Liu , M. Mei, A better asymptotic profile of Rosenau-Burgers equation  Appl. Math. Comput. 131 (2002) 147--170. [PDF]

[28]. H.-L. Li, P. Markowich, M. Mei, Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors , Proc. Royal Soc. Edinburgh, 132A (2002) 359--378. [PDF]

[27]. H.-L. Li, P. Markowich, M. Mei,Asymptotic behavior of subsonic entropy solutions of the isentropic Euler-Poisson equations, Quart. Appl. Math. (2002) 773--796. [PDF]

[26]. L. Hsiao, H.-L. Li, M. Mei,Convergence rates to superposition of two travelling waves of the solutions to a relaxation hyperbolic conservation laws with boundary effects, Math. Models Methods Appl. Sci. 11 (2001) 1143--1168. [PDF]

[25]. P. Marcati, M. Mei,Convergence to nonlinear diffusion waves for solutions of the initial boundary problem to the hyperbolic conservation laws with damping, Quart. Appl. Math. 58 (2000) 763--784. [PDF]

[24]. M. Mei, C. Schmeiser, Asymptotic profile of solution for the BBM-Burgers equation, Funkcial. Ekvac. 44 (2001) 151--170. [PDF]

[23]. S. Kinami, M. Mei, S. Omata, Convergence to diffusion waves of the solutions for Benjamin-Bona-Mahony-Burgers equations, Appl. Anal. Vol.75 No.3-4 (2000). [PDF]

[22]. M. Mei, B. Rubino, Convergence to traveling waves with decay rates for solutions of the initial boundary problem to a nonconvex relaxation model , J. Differential Equations, 159 (1999) 138--185. [PDF]

[21]. M. Mei, L^q-decay rates of solutions for Benjamin-Bona-Mahony-Burgers equations, J. Differential Equations, 158 (1999) 314--340. [PDF]

[20]. A. Matsumura, M. Mei, Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary , Arch. Rational Mech. Anal. 146 (1999) 1--22. [PDF]

[19]. M. Mei, Asymptotic behavior of solutions for a degenerate hyperbolic system of viscous conservation laws, Z. Angew. Math. Phys. 50 (1999) 617--637. [PDF]

[18]. M. Mei, Remark on stability of shock profiles for nonconvex scalar viscous conservation laws, Bull. Inst. Math. Acad. Sinica, 27 (1999) 213--226. [PDF]

[17]. M. Mei I-L. Chern,  Asymptotic stability of critical viscous shock waves for a degenerate hyperbolic viscous conservation laws, Commun. Partial Differential Equations, 23 (1998) 869-886. [PDF]

[16]. M. Mei, T. Yang, Convergence rates to travelling waves for a nonconvex relaxation model , Proc. Royal Soc. Edinburgh, 128A (1998) 1053-1068. [PDF]

[15]. M. Mei, Large-time behavior of solution for generalized Benjamin-Bona-Mahony-Burgers equations, Nonlinear Analysis, TMA 33 (1998) 699-714. [PDF]

[14]. M. Mei, A. Matsumura, Nonlinear stability of viscous shock profile for a non-convex system of viscoelasticity, Osaka J. Math. 34 (1997) 589-603. [PDF]

[13]M. Mei, Stability of traveling wave solutions for nonconvex equations of barotropic viscous gas, Osaka J. Math. 34 (1997) 303-318. [PDF]

[12]. M. Mei, K. Nishihara, Nonlinear stability of travelling waves for one dimensional viscoelastic materials with non-convex nonlinearity, Tokyo J. Math. 20(1997) 241-264. [PDF]

[11]. M. Mei, Long-time behavior of solution for Rosenau-Burgers equation (I), Appl. Anal. 63 (1996) 315-330. [PDF]

[10]. M. Mei, Long-time behavior of solution for Rosenau-Burgers equation (II), Appl. Anal. 68 (1998) 333--356. [PDF]

[9]. M. Mei (梅茗 メイ   ミン), Nonlinear Stability of Traveling WavesSolutions  for Non-Convex Viscous Conservation Laws (非凸性を持つ粘性的保存則に対する進行波解の非線形漸近安定性), Ph.D. Thesis (博士論文) , Kanazawa University (金沢大学), Japan, March of 1996.  [PDF]

[8]. M. Mei, Stability of shock profiles for nonconvex scalar viscous conservation laws, Math. Models Methods Appl. Sci. 5 (1995) 279-296. [PDF]

[7]. M. Mei, Y.-K. Xiao: Analysis for a mathematical model of the pattern formation on shells of mollusks, Appl. Math.-JCU (高校应用数学学报英文版 10B (1995) 411-418. [PDF]

[6]. 梅茗,黄福英, 高维非线性四阶抛物型方程初值问题全局解 (Global solutions of  Cauchy problem for  nonlinear fourth order parabolic equations with high dimension), 高校应用数学学报(中文版) (Applied Mathematics - A Journal of Chinese Universities),  1993年第8卷第1期 (Vol. 8, No.1, (1993)), 45--52. [PDF]

[5]. 梅茗,肖应昆, 具有非局部边值约束的中子迁移问题单调衰减解(Monotonic decay of solutions for nonlocal neutron transport equation with boundary effect),  应用数学(Mathematica Applicata),1992年第5卷第4期 (Vol. 5, No. 4, (1992)),109--112. [PDF]

[4]. 梅茗,曹德芬,肖应昆, 一类反应扩散系统解的全局稳定性和渐近性(Global asymptotic stability of solutions for a class of reaction-diffusion system), 数学物理学报Acta Math. Sci. ),1992年第12卷 增刊 (Vol. 12, Suppl.  (1992)),119--121. [PDF]

[3]. 梅茗, 高 维广义神经传播方程Cauchy问题整体光滑解 (Global smooth solutions of  the Cauchy problem  for the generalized equation of pulse transmission with higher dimension) 应用数学学报(中文版)(Acta Mathematicae  Applicatae  Sinica), 1991年04期 450-461. (硕士论文 master thesis) [PDF]

[2].  梅茗,Maxwell—Boltzmann方程非负解的极值原理和渐近性质 (Maximum principles and asymptotic properties of nonnegative solutions to the Maxwell-Boltzmann equation), 数学杂志(J. Math.(Wuhan))1990年第10卷第3期 341-348页. [PDF]

[1]. M. Mei, On nonlinear coupled reaction-diffusion equations, Acta Math. Sci. Series B(数学物理学报英文版), Vol. 9, No. 2 (1989) 163--174. [PDF]