Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth
Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth
复制标题
具有质量源模型肿瘤生长的非自主 Cahn-Hilliard-Darcy 系统的适定性和长期行为
DOI：
10.1016/j.jde.2015.04.009
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发表时间：
2015
影响因子：
2.4
通讯作者：
Zheng Songmu
中科院分区：
文献类型：
--
作者：
Jiang Jie;Wu Hao;Zheng Songmu
本文研究了具有非自治质量源项S的Cahn-Hilliard-Darcy系统的初边值问题。我们首先在二维和三维空间证明了整体弱解的存在性和唯一局部强解的存在性。然后，我们详细地研究了当空间维度为2时解的定性行为。更准确地说，我们证明了强解是全局存在的，并且定义了一个封闭的动力过程。然后，我们证明了平移有界质量源S的最小拉回吸引子的存在性。最后，当S是渐近自治的时，我们证明了任何整体弱/强解都收敛到单个定态，即t-→+∞。并给出了收敛速度的估计。
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→+∞. An estimate on the convergence rate is also given.