SINGULAR LIMIT OF VISCOUS CAHN-HILLIARD EQUATIONS WITH MEMORY AND DYNAMIC BOUNDARY CONDITIONS

被引：10
作者：
Gal, Ciprian G. [1 ]
Grasselli, Maurizio [2 ]
机构：
[1] Florida Int Univ, Dept Math, Miami, FL 33199 USA
[2] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2013年 / 18卷 / 06期
关键词：
Cahn-Hilliard equations; dynamic boundary conditions; global attractors; robust exponential attractors; memory relaxation; PHASE-FIELD SYSTEM; ROBUST EXPONENTIAL ATTRACTORS; SPINODAL DECOMPOSITION; ASYMPTOTIC-BEHAVIOR; HYPERBOLIC RELAXATION; GLOBAL ATTRACTORS; TIME BEHAVIOR; MODEL; CONVERGENCE; POTENTIALS;
D O I：
10.3934/dcdsb.2013.18.1581
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a modified Cahn-Hiliard equation where the velocity of the order parameter u depends on the past history of Delta mu, mu being the chemical potential with an additional viscous term alpha u(t); alpha > 0 : In addition, the usual no-flux boundary condition for u is replaced by a nonlinear dynamic boundary condition which accounts for possible interactions with the boundary. The aim of this work is to analyze the passage to the singular limit when the memory kernel collapses into a Dirac mass. In particular, we discuss the convergence of solutions on finite time-intervals and we also establish stability results for global and exponential attractors.
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页码：1581 / 1610
页数：30
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