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Stability of periodic stationary solutions of scalar conservation laws with space-periodic flux

Anne-Laure Dalibard (2011)

Journal of the European Mathematical Society

This article investigates the long-time behaviour of parabolic scalar conservation laws of the type ∂ t u + div y A ( y , u ) - Δ y u = 0 , where y ∈ ℝ N and the flux A is periodic in y . More specifically, we consider the case when the initial data is an L 1 disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u and the stationary solution behaves in L 1 norm like a self-similar profile for large times. The proof uses a time and space change of variables which is...

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Currently displaying 201 – 220 of 317