-In this paper we study the solutions of micromagnetism equation in thin domain and we prove that the magnetic field induced by the magnetisation behaves like the projection of the magnetic moment on the normal to the domain.

In this paper we study a model of ferromagnetic material governed by a nonlinear Laudau Lifschitz equation coupled with Maxwell equations. We prove the existence of weak solutions. Then we prove that all points of the |-limit set of any trajectories are solutions of the stationary model. Furthermore we derive rigourously the quasistatic model by an appropriate time average method. 1998Academic Press

We investigate totally linearly degenerate hyperbolic systems with relaxation. We aim to study their semilinear behavior, which means that the local smooth solutions cannot develop shocks, and the global existence is controlled by the supremum bound of the solution. In this paper we study two specific examples: the Suliciu-type and the Kerr-Debye-type models. For the Suliciu model, which arises from the numerical approximation of isentropic flows, the semilinear behavior is obtained using pointwise estimates of the gradient. For the Kerr-Debye systems, which arise in nonlinear optics, we show the semilinear behavior via energy methods. For the original Kerr-Debye model, thanks to the special form of the interaction terms, we can show the global existence of smooth solutions.

Abstract. In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.Mathematics Subject Classification. 35B35, 35K55.

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International audienceIn this work,we present a mathematical study of stability and controllability of one-dimensional network of ferromagnetic particles. The control is the magnetic field generated by a dipole whose position and whose amplitude can be selected. The evolution of the magnetic field in the network of particules is described by the Landau-Lifschitz equation. First, we model a network of ellipsoidal shape ferromagnetic particles. Then, we prove the stability of relevant configurations and discuss the controllability by the means of the external magnetic field induced by the magnetic dipole. Finally some numerical results illustrate the stability and the controllability results

in this paper we study a penalization method used to compute the flow of a viscous fluid around a thin layer of porous material. Using a BKW method, we perform an asymptotic expansion of the solution when a little parameter, measuring the thickness of the thin layer and the inverse of the penalization coefficient, tends to zero. We compare then this numerical method with a Brinkman model for the flow around a porous thin layer.