Analysis of singularities in elliptic equations : the Ginzburg-Landau model of superconductivity, the Lin-Ni-Takagi problem, the Keller-Segel model of chemotaxis, and conformal geometry

It is not a problem for us, since in our final proof of Theorem 1.2, we only need two independent smooth solutions wrt (d, γ 1 , γ 2 ) and having bounded behaviors at 0.. , 4, for

We introduce a “Coulombian renormalized energy” W which is a logarithmic type of interaction between points in the plane, computed by a “renormalization.” We prove various of

The stability region for the rhombic vortices, along with that for fundamental solitons, has been identified in the parameter space of the model, and generic scenarios of the

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

We consider a spherical superconductor in a uniform external field, and study vortices which appear near the lower critical field, the smallest value of the external field strength

The aim of this final section is to use the structure of the minimizers of the limiting functional F 0,g given by Theorem 4.3 to prove that minimizers of F ε,g 0 have the same