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Inégalités de Strichartz et équations d’ondes quasilinéaires

Hajer Bahouri, Jean-Yves Chemin (1997/1998)

Séminaire Équations aux dérivées partielles

Dans ce texte, notre but est de résoudre des équations d’ondes quasilinéaires pour des données initiales moins régulières que ce qu’impose les méthodes d’énergie. Ceci impose de démontrer des estimées de type Strichartz pour des opérateurs d’ondes à coefficients seulement lipschitziens.

Inertial manifolds for retarded second order in time evolution equations in admissible spaces

Cung The Anh, Le Van Hieu (2013)

Annales Polonici Mathematici

Using the Lyapunov-Perron method, we prove the existence of an inertial manifold for the process associated to a class of non-autonomous semilinear hyperbolic equations with finite delay, where the linear principal part is positive definite with a discrete spectrum having a sufficiently large distance between some two successive spectral points, and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to some admissible function spaces.

Infinite systems of first order PFDEs with mixed conditions

W. Czernous (2008)

Annales Polonici Mathematici

We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems...

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