Derivation of the Landau-Pekar Equations in a Many-Body Mean-Field Limit [0.03%]
Landau-Pekar方程的衍生在多体平均场极限中
Nikolai Leopold,David Mitrouskas,Robert Seiringer
Nikolai Leopold
We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is appro...
Alexandre Girouard,Antoine Henrot,Jean Lagacé
Alexandre Girouard
We study a new link between the Steklov and Neumann eigenvalues of domains in Euclidean space. This is obtained through an homogenisation limit of the Steklov problem on a periodically perforated domain, converging to a family of eigenvalue...
Martin Hairer,Étienne Pardoux
Martin Hairer
We consider a semilinear parabolic partial differential equation in R + × [ 0 , 1 ] d , where d = 1 , 2 or 3, with a highly oscillating random potential and either homogeneous Dirichlet or Neumann boundary condition. If the amplitu...
Nonlocal-to-Local Convergence of Cahn-Hilliard Equations: Neumann Boundary Conditions and Viscosity Terms [0.03%]
非局部到局部的收敛性：Cahn-Hilliard方程的Neumann边界条件和粘度项
Elisa Davoli,Luca Scarpa,Lara Trussardi
Elisa Davoli
We consider a class of nonlocal viscous Cahn-Hilliard equations with Neumann boundary conditions for the chemical potential. The double-well potential is allowed to be singular (e.g. of logarithmic type), while the singularity of the convol...
Shokhrukh Yu Kholmatov,Paolo Piovano
Shokhrukh Yu Kholmatov
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is cha...
Scott Armstrong,Samuel J Ferguson,Tuomo Kuusi
Scott Armstrong
We prove large-scale C ∞ regularity for solutions of nonlinear elliptic equations with random coefficients, thereby obtaining a version of the statement of Hilbert's 19th problem in the context of homogenization. The analysis proceed...
Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive Zone Models [0.03%]
连贯区模型中极小值自由边界的最优正则性和结构
L Caffarelli,F Cagnetti,A Figalli
L Caffarelli
We study optimal regularity and free boundary for minimizers of an energy functional arising in cohesive zone models for fracture mechanics. Under smoothness assumptions on the boundary conditions and on the fracture energy density, we show...
Exponential Time Decay of Solutions to Reaction-Cross-Diffusion Systems of Maxwell-Stefan Type [0.03%]
Maxwell-Stefan型反应-交叉扩散系统解的指数时间衰减性
Esther S Daus,Ansgar Jüngel,Bao Quoc Tang
Esther S Daus
The large-time asymptotics of weak solutions to Maxwell-Stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated. The diffusion matrix of the system is generally neither s...
Global Stability of Minkowski Space for the Einstein-Vlasov System in the Harmonic Gauge [0.03%]
调和坐标下爱因斯坦-弗拉索夫系统的米克沃斯基空间的全局稳定性问题
Hans Lindblad,Martin Taylor
Hans Lindblad
Minkowski space is shown to be globally stable as a solution to the massive Einstein-Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying th...
A Friedman,Bei Hu,Chuan Xue
A Friedman
Biofilms are formed when free-floating bacteria attach to a surface and secrete polysaccharide to form an extracellular polymeric matrix (EPS). A general model of biofilm growth needs to include the bacteria, the EPS, and the solvent within...