Semiconductor equations PA Markowich, CA Ringhofer, C Schmeiser Springer Science & Business Media, 2012 | 2326 | 2012 |

The stationary semiconductor device equations PA Markowich Springer Science & Business Media, 1985 | 764 | 1985 |

Homogenization limits and Wigner transforms P Gérard, PA Markowich, NJ Mauser, F Poupaud Communications on Pure and Applied Mathematics: A Journal Issued by the …, 1997 | 646 | 1997 |

Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation W Bao, D Jaksch, PA Markowich Journal of Computational Physics 187 (1), 318-342, 2003 | 575 | 2003 |

On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations A Arnold, P Markowich, G Toscani, A Unterreiter Taylor & Francis Group 26 (1-2), 43-100, 2001 | 449 | 2001 |

On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime W Bao, S Jin, PA Markowich Journal of Computational Physics 175 (2), 487-524, 2002 | 408 | 2002 |

Entropy dissipation methods for degenerate parabolicproblems and generalized sobolev inequalities JA Carrillo, A Jüngel, PA Markowich, G Toscani, A Unterreiter Monatshefte für Mathematik 133 (1), 1-82, 2001 | 372 | 2001 |

Kinetic models for chemotaxis and their drift-diffusion limits FACC Chalub, PA Markowich, B Perthame, C Schmeiser Nonlinear Differential Equation Models, 123-141, 2004 | 268 | 2004 |

Global solutions to the coupled chemotaxis-fluid equations R Duan, A Lorz, P Markowich Communications in Partial Differential Equations 35 (9), 1635-1673, 2010 | 238 | 2010 |

Numerical study of time-splitting spectral discretizations of nonlinear Schrödinger equations in the semiclassical regimes W Bao, S Jin, PA Markowich SIAM Journal on Scientific Computing 25 (1), 27-64, 2003 | 235 | 2003 |

The nonlinear Schrödinger equation G Fibich Springer, 2015 | 204 | 2015 |

Semiconductor device modelling from the numerical point of view SJ Polak, C Den Heijer, WHA Schilders, P Markowich International Journal for Numerical Methods in Engineering 24 (4), 763-838, 1987 | 201 | 1987 |

Quantum hydrodynamics, Wigner transforms, the classical limit I Gasser, PA Markowich Asymptotic Analysis 14 (2), 97-116, 1997 | 191* | 1997 |

On a one-dimensional steady-state hydrodynamic model for semiconductors P Degond, PA Markowich Applied Mathematics Letters 3 (3), 25-29, 1990 | 185 | 1990 |

The three‐dimensional wigner‐poisson problem: Existence, uniqueness and approximation F Brezzi, PA Markowich Mathematical Methods in the Applied Sciences 14 (1), 35-61, 1991 | 174 | 1991 |

On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis PA Markowich, C Villani Mat. Contemp 19, 1-29, 2000 | 168 | 2000 |

A Wigner‐function approach to (semi) classical limits: Electrons in a periodic potential PA Markowich, NJ Mauser, F Poupaud Journal of Mathematical Physics 35 (3), 1066-1094, 1994 | 166 | 1994 |

Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior M Di Francesco, A Lorz, PA Markowich Discrete & Continuous Dynamical Systems 28 (4), 1437, 2010 | 160 | 2010 |

Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders B Düring, P Markowich, JF Pietschmann, MT Wolfram Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2009 | 158 | 2009 |

Mathematical and computational methods for semiclassical Schrödinger equations S Jin, P Markowich, C Sparber University of Illinois at Chicago, 2011 | 153 | 2011 |