Codina Cotar,Gero Friesecke,Brendan Pass
Codina Cotar
We introduce and analyze symmetric infinite-body optimal transport (OT) problems with cost function of pair potential form. We show that for a natural class of such costs, the optimizer is given by the independent product measure all of who...
Stable spike clusters for the precursor Gierer-Meinhardt system in [Formula: see text] [0.03%]
广义Gierer-Meinhardt系统在R²中稳定.spike簇的解
Juncheng Wei,Matthias Winter,Wen Yang
Juncheng Wei
We consider the Gierer-Meinhardt system with small inhibitor diffusivity, very small activator diffusivity and a precursor inhomogeneity. For any given positive integer k we construct a spike cluster consisting of k spikes which all approac...
Manh Hong Duong,Agnes Lamacz,Mark A Peletier et al.
Manh Hong Duong et al.
In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational evolution...
Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media [0.03%]
准周期双尺度均匀化和高对比度介质中的有效空间色散
Shane Cooper
Shane Cooper
The convergence of spectra via two-scale convergence for double-porosity models is well known. A crucial assumption in these works is that the stiff component of the body forms a connected set. We show that under a relaxation of this assump...
Melanie Rupflin,Peter M Topping
Melanie Rupflin
We analyse the fine convergence properties of one parameter families of hyperbolic metrics that move always in a horizontal direction, i.e. orthogonal to the action of diffeomorphisms. Such families arise naturally in the study of general c...
Matthias Erbar,Jan Maas,Melchior Wirth
Matthias Erbar
We consider the space of probability measures on a discrete set X , endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset Y ⊆ X , it is natural to ask whether they can be connected by...
José A Carrillo,Franca Hoffmann,Edoardo Mainini et al.
José A Carrillo et al.
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 model of chemotaxis. We analyse the regi...
Global existence of Dirac-wave maps with curvature term on expanding spacetimes [0.03%]
具曲率项的Dirac-波映射在时空上的整体存在性问题
Volker Branding,Klaus Kröncke
Volker Branding
We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence re...
Andrea Colesanti,Monika Ludwig,Fabian Mussnig
Andrea Colesanti
A classification of [Formula: see text] contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measure is characterized. In addition, a new [Formula:...
On the structure of solutions to a class of quasilinear elliptic Neumann problems. Part II [0.03%]
一类拟线性椭圆型纽曼问题解的结构(二)
Chunshan Zhao,Yi Li
Chunshan Zhao
We continue our work (Y. Li, C. Zhao in J Differ Equ 212:208-233, 2005) to study the structure of positive solutions to the equation epsilon(m) Delta(m)u - u(m-1) + f(u) = 0 with homogeneous Neumann boundary condition in a smooth bounded do...