Hydrodynamic Limit for the Ginzburg-Landau $ablaφ$ Interface Model with a Conservation Law

Journal of Mathematical Sciences

Nishikawa, Takao¹ 

关键词: Hydrodynamic Limit;    Ginzburg-Landau Model;    Effective Interfaces;    Massless Fields;    Surface Diffusion;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

HydrodynamiclimitfortheGinzburg-Landau$ablaφ$interfacemodelwasestablishedin[5]undertheperiodicboundaryconditions.Thispaperextendstheirresultstothemodifieddynamicswhichpreservethetotalvolumeofeachmicroscopicphase.Nonlinearpartialdifferentialequationoffourthorder%[frac{partialh}{partialt}=-Δleft[diveleft{(ablaσ)(ablah(t,θ))ight}ight],θin{mathbbT}^dequiv[0,1)^d,,t>0]%isderivedasthemacroscopicequation,where$σ=σ(u)$isthesurfacetensionofthesurfacewithtilt$uineal^d$.Themaintoolis$H^{-2}$-method,whichisamodificationof$H^{-1}$-methodusedin[5].TheGibbsmeasuresassociatedwiththedynamicsarecharacterized.

【 授权许可】

Unknown