LIMITING MOTION FOR THE PARABOLIC GINZBURG-LANDAU EQUATION WITH INFINITE ENERGY DATA

We would like to draw the attention of the reader that in the scalar case considered here the exact form of the optimal profile plays a central role in the analysis. We will

Null controllability of the complex Ginzburg–Landau equation Contrôlabilité à zéro de l’équation de Ginzburg–Landau complexe.. Lionel Rosier a,b, ∗ , Bing-Yu

There is a convenient variational setting for the periodic Ginzburg–Landau equations, we may refer to [20,13] for a mathematically oriented presentation of this setting, the

For a sufficiently large applied magnetic field and for all sufficiently large values of the Ginzburg–Landau parameter κ = 1/ε, we show that minimizers have nontrivial

Vol. - In this paper we study the structure of certain level set of the Ginzburg-Landau functional which has similar topology with the configuration space. As an

We find a vanishing gradient type property and then we obtain the renormalized energy by Bethuel, Brezis and Helein’s shrinking.. holes

Using various elliptic estimates, we are able to relate, in the same spirit, local estimates for the gradient of the modulus to the potential as follows..

For the convenience of the reader, we indicate in Section 2 below an independent proof of Proposition 1.1; (1.8) and (1.9) are true for finite-energy states, whereas the zero