## Nonlinear Partial Differential Equations and Their Applications: College de France Seminar, Volume 14This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields. |

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### Contents

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analysis of the system | 69 |

6 Détermination de conditions aux limites en mer ouverte par une méthode de contrôle optimal | 103 |

7 Effective diffusion in vanishing viscosity | 133 |

8 Vibration of a thin plate with a rough surface | 147 |

15 Uniqueness and stability in the Cauchy problem for Maxwell and elasticity systems | 329 |

16 On the unstable spectrum of the Euler equation | 351 |

17 Décomposition en profils des solutions de léquation des ondes semi linéaire critique á lextérieur dun obstacle strictement convexe | 367 |

18 Upwind discretizations of a steady gradetwo fluid model in two dimensions | 393 |

19 Stability of thin layer approximation of electromagnetic waves scattering by linear and non linear coatings | 415 |

20 Remarques sur la limite α 0 pour les fluides de grade 2 | 457 |

21 Remarks on the Kompaneets equation a simplified model of the FokkerPlanck equation | 469 |

22 Singular perturbations without limit in the energy space Convergence and computation of the associated layers | 489 |

9 Anisotropy and dispersion in rotating fluids | 171 |

10 Integral equations and saddle point formulation for scattering problems | 193 |

11 Existence and uniqueness of a strong solution for nonhomogeneous micropolar fluids | 213 |

12 Homogenization of Dirichlet minimum problems with conductor type periodically distributed constraints | 243 |

13 Transport of trapped particles in a surface potential | 273 |

14 Diffusive energy balance models in climatology | 297 |

23 Optimal design of gradient fields with applications to electrostatics | 509 |

24 A blackbox reducedbasis output bound method for noncoercive linear problems | 533 |

25 Simulation of flow in a glass tank | 571 |

26 Control localized on thin structures for semilinear parabolic equations | 591 |

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Stabilité des ondes de choc de viscosité qui peuvent être caractéristiques | 647 |