We continue the study of [AS] on the Chapman-Rubinstein-Schatzman-E evolution model for superconductivity, viewed as a gradient flow on the space of measures equipped with the quadratic Wasserstein… (More)

Abstract: For a functional defined on the class of closed onedimensional connected subsets of R we consider the corresponding minimization problem and we give suitable first order necessary… (More)

We establish some decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation ut(t)− β∆u(t)− ∫ ∞ 0 k(s)∆u(t−… (More)

We consider an energy functional on measures in R arising in superconductivity as a limit case of the well-known Ginzburg Landau functionals. We study its gradient flow with respect to the… (More)

In this paper we study a class of non linear diffusion equations in a Hilbert space X, ∂tμt −∇ · (∇(L ◦ ρt)γ) = 0 in X × (0,+∞), with respect to a log-concave reference probability measure γ. We… (More)

We consider macroscopic descriptions of particles where repulsion is modelled by non-linear power-law diffusion and attraction by a homogeneous singular kernel leading to variants of the Keller-Segel… (More)

We consider, in an abstract setting, an instance of the ColemanGurtin model for heat conduction with memory, that is the Volterra integrodifferential equation ∂tu(t)− β∆u(t)− ∫ t 0 k(s)∆u(t− s)ds =… (More)

We prove that the signed porous medium equation can be regarded as limit of an optimal transport variational scheme, therefore extending the classical result for positive solutions of [13] and… (More)

In this paper we study the compact and convex sets K ⊆ Ω ⊆ R that minimize ∫ Ω dist(x,K) dx + λ1V ol(K) + λ2Per(K) for some constants λ1 and λ2, that could eventually be zero. We compute in… (More)