Montreal Sunset

  Montreal Sunset


Selected 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 CEGEP International.  

      NSERC fundings
      1.  ``Sharp traveling waves for degenerate diffusion equations with delay",  NSERC Individual Discovery Grant 2022-03374,    years: 2022-2027.  $135,000
      2. ``Non-monotone traveling waves for reaction-diffusion equations with delay", NSERC Individual Discovery Grant 354724-2016,    years: 2016-2022.  $108,000      
       3.   ``Damped Euler-Poisson equations and nonlinear diffusion waves", NSERC Individual Discovery Grant 354724-2011,   years: 2011-2016.  $50,000           
      4.  ``Phase transitions and partial differential equations of mixed type", NSERC Individual Discovery Grant 354724-2008,    years: 2008-2011.  $42,000

      FRQNT fundings:
      5.  ``Euler-Poisson équations de modèles semi-conducteurs avec limite sonique " FRQNT grant 256440,  years 2018-2021.     $96,000     
      6. ``Stabilitédes ondes oscillatoires de déplacement pour les équations de réaction-diffusion à retardement ",  FRQNT grant 192571, years: 2015-2018.  $108,000       
      7. ``Études des équations d'évolution non linéaires de la dynamique des fluides", FRQNT grant 164832,    years: 2012-2015.  $84,000    
   
     CEGEP International
      8. ``Collaboration internationale de la recherche scientifique à Beijing ", Fédération de  cégeps, year: 2014-2015.   $3,000    
      9. ``Collaboration internationale de la recherche scientifique à Italie ", CEGEP International,   year: 2013-2014.     $3,000
      10. ``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 five SCI journals and the others:

         Associate editor, Applicable Analysis, 2014-present  (SCI)

         Associate editor, International Journal of Numerical Analysis and Modeling, 2015-present (SCI)

         Editorial board,  Communications in Analysis and Mechanics, 2023-present (SCI)

       Editorial board, Advance in Mathematical Physics, 2010-present  (SCI)

       Editorial board, Mathematics published by MDPI, 2018-present (SCI)

       Editorial advisory board, Advances in Differential Equations and Control Process, 2010-present

       Associate editor, International Journal of Numerical Analysis and Modeling, Series B, 2010-2015

       Editor board, Abstract and Applied Analysis, 2008-2018

 

I have published more than 130 papers in academic journals, most of them appear in the top journals of PDEs research field, like Archiv. Rational Mech. Anal., SIAM J. Math. Anal., Commun. PDEs, J. Differetial Equations, Math. Method Model. Appl. Sci. and so on. 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). I am also one of the top authors with 14 papers in SIAM J. Math. Anal., with 26 papers in  J. Differential Equations, and with 3 papers in J. Nonlinear Science, listed by AMS MathSciNet. Here are some selected papers. For the full list of publication, please click here,  for  reviews of my publications in Mathematical Reviews, look here, and for citations of my publications, please look at Google Scholar for my own site. 

Selected papers  (click  [PDF] at the end of each item to download the paper):

[85]  C. Xie, S. Fang, M. Mei,  and Y. Qin, Asymptotic behavior for the fast diffusion equation with absorption and singularity,   J. Differential Equations, 414 (2025), 722-745.  [PDF]

[84]  Y.-H. Feng, R. Li, M. Mei,  and S. Wang, Global convergence rates in zero-relaxation limits for non-isentropic Euler-Maxwell equations,   J. Differential Equations, 414 (2025), 372-404.  [PDF]

[83]  Y.-H. Feng, H. Hu, M. Mei, G. Tsotsgerel, and G. Zhang, Relaxation time limits of subsonic steady states for multimensional  hydrodynamic model of semiconductors,  SIAM J. Math. Anal.. 56 (2024), 6933-6962. [PDF]

[82]  T. Xu,  S. Ji, M. Mei, and J. Yin,  Global Stability of Sharp Traveling Waves for Combustion Model with Degenerate Diffusion,  J. Dyn. Differential Equations.  (2024), https://doi.org/10.1007/s10884-024-10401-7. [PDF]

[81]  T. Xu,  S. Ji, M. Mei, and J. Yin, Convergence to sharp traveling waves of soutions for Burgers-Fisher-KPP equations with degenerate diffusion, J. Nonlinear Sci.  34  (2024), article #44, [PDF] https://doi.org/10.1007/s00332-024-10021-x

[80]  Y.-H. Feng, H. Hu, M. Mei, and  Y. Zhu, 3D full hydrodynamic model for semiconductor optoelectronic devices: stability of thermal equilibrium states,    J. Differential Equations, 403 (2024), 465-509. .[PDF]

[79]   Y.-H. Feng, H. Hu, M. Mei,  Y.-J. Peng, and G. Zhang, Relaxation time limits of subsonic steady states for hydrodynamic model of semiconductors with sonic or non-sonic boundary,  SIAM J. Math. Anal.. 56 (2024), 3452-3477. [PDF]

[78]  Y.-H. Feng, H. Hu,  and  M. Mei, Structural stability of subsonic steady states to the hydrodynamic model for semiconductors with sonic boundary,   Nonlinearity, 37 (2024), 025020. https://doi.org/10.1088/1361-6544/ad1c2e  [PDF]

 [77]  S. Zhao,  M. Mei, and K. Zhang, Structural stability of subsonic steady-states to the bipolar Euler-Poisson equations with degenerate boundary,   J. Differential Equations,   395 (2024), 125-152. [PDF]. 

[76]  R. Peng, J. Li,  M. Mei, and K. Zhang, Characteristic boundary layers in the vanishing viscosity limit for the Hunter-Saxton equation,   J. Differential Equations,   386 (2024), 164-195. [PDF]. 

[75]  S. Li,  M. Mei, K. Zhang,  and G. Zhang, Subsonic steady-states for bipolar hydrodynamic model for semiconductors,   J. Differential Equations,   382 (2024), 274-301. [PDF]. 

[74]   J. Xu, M. Mei, and S. Nishibata,  Structural stability of radial interior subsonic steady-states to n-D Euler-Poisson system of semiconductor models with sonic boundary,  SIAM J. Math. Anal.. 55 (2023), 7741--7761. [PDF]

[73]   L.  Chen, M. Mei, and G. Zhang,  Radially symmetric spiral flows of the compressible Euler-Poisson system for semiconductors,   J. Differential Equations,   373 (2023), 359-388. [PDF]. 

[72]   L.  Chen, D. Li, M. Mei, and G. Zhang,  Quasi-neutral limit to steady-state hydrodynamic model of semiconductors with degenerate boundary,   SIAM J. Math. Anal.. 55 (2023), 2813--2837. [PDF]

[71]  Y.-H. Feng, X. Li,  M. Mei, and S. Wang,  Zero-Relaxation Limits of the Non-Isentropic Euler–Maxwell System for Well/Ill-Prepared Initial Data, J. Nonlinear Sci.  33 (2023), article # 71. [PDF]

[70]  H. Hu, H. Li,  M. Mei, and L. Yang, Structural stability of subsonic solutions to a steady hydrodynamic model for semiconductors: From the perspective of boundary data, Nonlinear Anal. Real World Appl.   74 (2023), paper #103937.   [PDF]

 [69].  S. Ji and M. Mei,  Optimal decay rates of the compressible Euler equations with time-dependent damping in R^n Rn: (II) over-damping case,   SIAM J. Math. Anal.. 55 (2023), 1048-1099.  [PDF]  arXiv: 2006.00403

 [68].  S. Ji and M. Mei, Optimal decay rates of the compressible Euler equations with time-dependent damping in R^n Rn: (I) under-damping case, J. Nonlinear Sci.  33 (2023), article # 7.  https://doi.org/10.1007/s00332-022-09865-y  [PDF] .

[67]   R. Huang, M. Mei, Z. Wang,  Threshold convergence results for a nonlocal time-delayed diffusion equation,    J. Differential Equations,   364 (2023), 76-106. [PDF]. 

[66]   Y.-H. Feng, M. Mei, and G. Zhang,   Nonlinear structural stability and linear dynamic instability of transonic steady-states to a hydrodynamic model for semiconductors,  J. Differential Equations, 344  (2023),  131-171.  [PDF] arXiv.2202.03475.

[65]   M. Mei, T. Xu, J. Yin,   Monotone reducing mechanism in delayed population model with degenerate diffusion,   J. Differential Equations,  342 (2023), 490-500.  [PDF]

[64]  H.-L. Li,  M. Mei, J. Xu, Asymptotic behavior of solutions to the unipolar hydrodynamic model of semiconductors with time-dependent damping in bounded domain,  Commun. Math. Sci.,   21 (2023), no. 1, 255–280.  [PDF]

[63]  T. Xu, S. Ji, M. Mei, J. Yin, Critical sharp front for doubly nonlinear degenerate diffusion equations with time delay,  Nonlinearity, 35 (2022), 3358-3384. [PDF]

[62]  T. Xu, S. Ji, M. Mei, J. Yin, Propagation speed of degenerate diffusion equations with time delay,  J. Dyn. Differential Equations, 34 (2022), https://doi.org/10.1007/s10884-022-10182-x. [PDF]

[61]  R. Peng, J. Li, M. Mei, K. Zhang, Convergence rate of the vanishing viscosity limit for the Hunter-Saxton equation in the half space,   J. Differential Equations,  328 (2022), 202-227.  [PDF]

[60]   R. Meng, L.-S. Mai, M. Mei,  Free boundary value problem for  damped Euler equations and related models with vacuum,    J. Differential Equations,  321 (2022), 349-380. (32 pages). [PDF]

[59]  M. Mei and  Y. Wang,  Existence of traveling wave fronts of delayed Fisher-type equations with degenerate nonlinearities, Appl. Math. Lett., 129 (2022), Paper No. 107937, 8 pp.  [PDF]

[58].  Hui Sun, M. Mei, Kaijun Zhang,  Sub-exponential convergence to steady-states for  1-D Euler-Poisson equations with time-dependent damping,  Commun. Math. Sci.,  Vol. 20,  (2022). [PDF]

[57].  Liang Chen, M. Mei, Guojing Zhang and Kaijun Zhang,  Transonic steady-states of Euler-Poisson equations for semiconductor models with sonic boundary in multiple dimensions,   SIAM J. Math. Anal.. Vol. 54, No. 1, (2022), pp. 363--388  [PDF]

 [56].  Yue-Hong Feng, Xin Li,  M. Mei, Shu Wang, Yang-Cheng Cao, Convergence to Steady-States of Compressible Navier–Stokes–Maxwell Equations,   J. Nonlinear Science,   Vol. 32,， （2022），Article 2 (32 pages).  https://doi.org/10.1007/s00332-021-09763-9  [PDF]

[55].  La-Su Mai and  M. Mei, Newtonian limit for the relativistic Euler-Poisson equations with vacuum,   J. Differential Equations,  313 (2022), 336-381. (46 pages). [PDF]

[54].  Changchun Liu,  M. Mei, Jiaqi Yang, Global stability of traveling waves for nonlocal time-delayed degenerate diffusion equation,   J. Differential Equations,  306 (2022), 60-100. (41 pages). [PDF]

[53].  Hui Sun, M. Mei, Kaijun Zhang,  Sub-exponential convergence to steady-states for  1-D Euler-Poisson equations with time-dependent damping,  Commun. Math. Sci.,  Vol. 20. (2022).

 [52]  Yue-Hong Feng, Xin Li,  M. Mei, Shu Wang,  Asymptotic decay of bipolar isentropic/non-isentropic compressible Navier-Stokes-Maxwell systems,   J. Differential Equations,  301 (2021), 471-542. (72 pages). [PDF]

[51]  Mengmeng Wei, M. Mei, Guojing Zhang and Kaijun Zhang,  Smooth transonic steady-states of hydrodynamic model for semiconductors,   SIAM J. Math. Anal.. Vol. 53, No.4, (2021), 4908-4932.  [PDF]

[50].  Stability of steady-states for 3-D hydrodynamic model of unipolar semiconductor with Ohmic contact boundary in hollow ball (with Xiaochun Wu, Yongqian Zhang),   J. Differential Equations,  277 (2021), 57-113. (57 pages). [PDF]

[49].  Existence and uniqueness for a stationary hybrid quantum hydrodynamical model with general pressure functional (with F. di Michele, B. Rubino, and R. Sampalmieri, ),   Commun. Math. Sci.,  Vol 19, No. 8,  (2021), 2049-2079.  [PDF]

[48].   Large-Time Behavior of Solutions to Cauchy Problem for Bipolar Euler-Poisson System with Time-Dependent Damping in Critical Case (with Liping Luan, Bruno Rubino, Peicheng Zhu),  Commun. Math. Sci., 19  (2021), 1207--1231 .  [PDF].

[47].  Haitong Li, Jingyu Li, M. Mei, and Kaijun Zhang, Optimal convergence rate to nonlinear diffusion waves for Euler equations with critical overdamping,  Appl. Math. Lett.  113 (2021), 106882. [PDF]

[46].  Subsonic and supersonic steady-states of bipolar hydrodynamic model of semiconductors with sonic boundary (with Pengcheng Mu and Kaijun Zhang), Commun. Math. Sci., Vol. 18, No. 7,  (2020), pp. 2005--2038.  [PDF].

[45].  Novel convergence to steady-state for Nicholson’s blowflies equation with Dirichlet boundary (with Jiaqi Yang and Yang Wang),  Appl. Math. Lett.  114 (2021), 106895. [PDF]

[44].  Optimal convergence rate to nonlinear diffusion waves for Euler equations with critical overdamping (with Haitong Li, Jingyu Li and Kaijun Zhang),  Appl. Math. Lett.  113 (2021), 106882. [PDF]

[43].  Asymptotic behavior of solutions to Euler equations with Ttme-dependent damping in critical case (with Shifeng Geng and Yanping Lin),   SIAM J. Math. Anal.  Vol. 52,  (2020),  1463--1488. [PDF]

[42].  Variational approach of  critical sharp front speeds in density-dependent diffusion model with time delay （with Tianyuan Xu, Shanming Ji, and Jingxue Yin),  Nonlinearity,  33 (2020), 4013--4029.  [PDF]   arXiv: 1909.11751.

[41].   Sharp oscillatory traveling waves of structured population dynamics model with degenerate diffusion   （with Tianyuan Xu, Shanming Ji, and Jingxue Yin),  J. Differential Equations,  269 (2020), 8882--8917.  [PDF].  arXiv:1909.11747

[40]. On a chemotaxis model with degenerate diffusion: Initial shrinking, eventual smoothness and expanding （with Tianyuan Xu, Shanming Ji, and Jingxue Yin), J. Differential Equations, 268 (2020), 414-446.  [PDF]

[39].  Steady hydrodynamic model of semiconductors with sonic boundary and transonic doping profile (with Liang Chen, Guojing Zhang and Kaijun Zhang),   J. Differential Equations, 269 (2020), 8173--8211.  [PDF].

[38].  Global and blow-up solutions to compressible Euler equations with time-dependent damping (with S. Chen, H. Li, J. Li, and K. Zhang),   J. Differential Equations, 268 (2020), 5035-5077.  [PDF]

[37]. Dirichlet problem for the Nicholson's blowflies equation with density-dependent diffusion (with Shanming Ji, and Zejia Wang), Appl. Math. Lett.  103 (2020), 106191. [PDF]

[36].  Stationary solutions for a new hybrid quantum model for semiconducotrs with discontinuous pressure functional and relaxation time  (with F. Di Michele,  B. Rubino and R. Sampalmieri), Math. Mech. Solids.  24 (2019),  2096-2115.  https://doi.org/10.1177/1081286518814289 | [PDF]  

[35].  Early and late stage profiles for a new chemotaxis model with density-dependent jump probability and quorum-sensing mechanisms,(with Tianyuan Xu, Shanming Ji, Chunhua Jin,  and Jingxue Yin) , Math. Biosci.  Engin. Vol. 15, No. 6 (2018）, 1345--1385.  [PDF]  

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

[33].  Existence and stability of traveling waves for degenerate reaction-diffusion equation with time delay (with R. Huang, C. Jin and  J. Yin),  J. Nonlinear Science,   28,   (2018) 1011-1042.  [PDF].  https://doi.org/10.1007/s00332-017-9439-5

[32].  Steady hydrodynamic model of semiconductors with sonic boundary: (II) Supersonic doping profile (with J. Li, G. Zhang, and K. Zhang),  SIAM J. Math. Anal.   50  (2018),  718--734.  [PDF]  

[31].  Steady hydrodynamic model of semiconductors with sonic boundary: (I) Subsonic doping profile (with J. Li, G. Zhang, and K. Zhang),  SIAM J. Math. Anal.   49  (2017), pp. 4767--4811  [PDF]  

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

[29].  Asymptotic analysis on a bipolar quantum semiconductor hydrodynamic model (with H. Hu and K. Zhang,), Commun. Math. Sci., 14, No. 8 (2016), pp. 2331-2371. [PDF]

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

[27].  Asymptotic profile of a parabolic-hyperbolic system with boundary effect arising from tumor angiogenesis (with H. Peng and Z.-A. Wang), J. Differential Equations,  259 (2015), 5168--5191. [PDF]

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

[25].  Exponential  stability of non-monotone traveling waves for Nicholson's blowflies equation (with Chi-Kun Lin, Chi-Tien Lin and Yaping Lin),  SIAM J. Math. Anal, 46, (2014), pp. 1053-1084. [PDF] [Most cited paper]

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

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

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

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

[20]. Global stability of monostable traveling waves for  nonlocal time-delayed reaction-diffusion equations (with C.H. Ou and X.-Q. Zhao),  SIAM J. Math. Anal.,  42,  (2010), 2762--2790. [PDF]  & 44  (2012), pp 538--540. [Erratum]

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

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

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

[16]. 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 Equations, 247 (2009), 495--510.  [PDF] [Most cited paper]

[15]. 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]

[14]. Novel stability results for travelling wavefronts in an age-structured reaction-diffusion population model (with Y. S. Wong),  Math. Biosci. Engin., 6  (2009), 743--752. [PDF]

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

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

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

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

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

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

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

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

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

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

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

[2].  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]

[1]. 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]