Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth

CORC > 武汉物理与数学研究所 > 中国科学院武汉物理与数学研究所 > 数学物理与应用研究部

	Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth
	Jiang, Jie 1; Wu, Hao 2,3; Zheng, Songmu 4
刊名	JOURNAL OF DIFFERENTIAL EQUATIONS
	2015-10-05
卷号	259 期号:7 页码:3032-3077
关键词	Cahn-Hilliard-Darcy system Non-autonomous Well-posedness Long-time behavior
英文摘要	In this paper, we study an initial boundary value problem of the Cahn-Hilliard-Darcy system with a non-autonomous mass source term S that models tumor growth. We first prove the existence of global weak solutions as well as the existence of unique local strong solutions in both 2D and 3D. Then we investigate the qualitative behavior of solutions in details when the spatial dimension is two. More precisely, we prove that the strong solution exists globally and it defines a closed dynamical process. Then we establish the existence of a minimal pullback attractor for translated bounded mass source S. Finally, when S is assumed to be asymptotically autonomous, we demonstrate that any global weak/strong solution converges to a single steady state as t --> +infinity. An estimate on the convergence rate is also given. (C) 2015 Elsevier Inc. All rights reserved.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Mathematics
研究领域[WOS]	Mathematics
关键词[WOS]	HELE-SHAW CELL ; SEMILINEAR EVOLUTION-EQUATIONS ; PHASE-FIELD MODEL ; PULLBACK ATTRACTORS ; ASYMPTOTIC-BEHAVIOR ; DYNAMICAL-SYSTEMS ; ORDER-PARAMETER ; FREE-ENERGY ; CONVERGENCE ; FLOW
收录类别	SCI
语种	英语
WOS记录号	WOS:000357903500017
公开日期	2015-09-15
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/7824]
专题	武汉物理与数学研究所_数学物理与应用研究部
作者单位	1.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei Province, Peoples R China 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 3.Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China 4.Fudan Univ, Inst Math, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Jiang, Jie,Wu, Hao,Zheng, Songmu. Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2015,259(7):3032-3077.
APA	Jiang, Jie,Wu, Hao,&Zheng, Songmu.(2015).Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth.JOURNAL OF DIFFERENTIAL EQUATIONS,259(7),3032-3077.
MLA	Jiang, Jie,et al."Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth".JOURNAL OF DIFFERENTIAL EQUATIONS 259.7(2015):3032-3077.