WELL-POSEDNESS AND LONG-TIME BEHAVIOUR FOR THE NON-ISOTHERMAL CAHN-HILLIARD EQUATION WITH MEMORY

被引：16

作者：

Pruess, Jan ^{[1
]}

Vergara, Vicente ^{[2
]}

Zacher, Rico ^{[1
]}

机构：

[1] Univ Halle Wittenberg, Inst Math, D-06120 Halle, Germany

[2] Univ Tarapaca, Inst Alta Invest, Arica, Chile

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 26卷 / 02期

关键词：

Maximal regularity; integro-differential equations; phase field system with memory; Cahn-Hilliard equation with memory; Lojasiewicz-Simon inequality; convergence to equilibrium; PHASE-FIELD SYSTEM; ASYMPTOTIC-BEHAVIOR; MAXIMAL REGULARITY; STEADY-STATES; L-P; CONVERGENCE; STABILITY;

D O I：

10.3934/dcds.2010.26.625

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a temperature dependent phase field model with memory. The case where both the equation for the temperature and that for the order parameter is of fractional time order is covered. Under physically reasonable conditions on the nonlinearities we prove global well-posedness in the L-p setting and show that each solution converges to a steady state as time goes to infinity.

引用

页码：625 / 647

页数：23

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