## Frontiers in Mathematical Analysis and Numerical Methods: In Memory of Jacques-Louis LionsThis invaluable volume is a collection of articles in memory ofJacques-Louis Lions, a leading mathematician and the founder of theContemporary French Applied Mathematics School. The contributions havebeen written by his friends, colleagues and students, including CBardos, A Bensoussan, S S Chern, P G Ciarlet, R Glowinski, Gu Chaohao, B Malgrange, G Marchuk, O Pironneau, W Strauss, R Temam, etc |

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### Contents

Always Remembered | 19 |

Regularity Theory for Systems of Partial Differential Equations | 47 |

Sensitivity of Darcys Law to Discontinuities | 71 |

On the Connection in Finsler Space | 97 |

On the Uniqueness of the Weak Solutions of a Quasilinear | 131 |

Regularity Results for Linear Elliptic Problems Related | 149 |

Local Exact Boundary Controllability for a Class of Quasilinear | 171 |

On Nonlinear Differential Galois Theory | 185 |

Quadrilateral Mesh | 207 |

On the Hyperbolic Obstacle Problem of First Order | 233 |

Instability of Traveling Waves of | 253 |

Complexity of Large Time Behaviour of Evolution Equations | 267 |

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2000 MR Subject a.e. in Q algebra Anal analysis Applied Mathematics approximation assume assumption asymptotic Bi-Section Condition boundary condition bounded Cauchy problem coincidence set compact computed conservation laws consider convergence convex defined degenerate mesh denote derivative dimension Dirichlet domain elliptic entropy solution estimate Euler equation finite element method flow foliation Fudan University function global Glowinski heat equation Hence homogenization hyperbolic systems implies initial data instability integral Jacques-Louis Lions Jn Jn Kuramoto-Sivashinsky equation L2 norm Lemma linear Math mean field equation Navier-Stokes equations nonconforming nonlinear numerical obstacle problem obtain omega-limit operator Paris partial differential equations positive constant primitive equations proof of Theorem prove quasilinear hyperbolic systems Remark resp satisfies scalar conservation laws Section semigroup sequence SIAM small C1 norm space stability subset Theorem 1.1 theory tion topology transversal unique solution value problem variational inequalities vector field weak-star weakly