论文标题
Cahn-Hilliard肿瘤生长模型的长期动力学与趋化性
Long-time Dynamics for a Cahn-Hilliard Tumor Growth Model with Chemotaxis
论文作者
论文摘要
描述肿瘤生长过程的数学模型已由几位作者提出，以了解癌症的发展方式和开发新的治疗方法。在这项研究中，其目的是研究两相弥漫性接口模型的长期行为，该模型在[11]中提出，将肿瘤组织建模为癌细胞和健康细胞的混合物。到目前为止，对该模型的长期行为的研究已经忽略了趋化性和主动转运，这对肿瘤生长产生了显着影响。在这项研究中，我们的主要目的是通过趋化性和主动运输研究该模型。我们证明了整个相位空间$ h^1（ω）\ times l^2（ω）$中问题的弱解的渐近紧凑性。我们在通过群众保护表示的相空间中建立了全球吸引子的存在。我们还证明，全球吸引子等于从固定点的集合中发出的不稳定流形。此外，我们获得了全球吸引子具有有限的分形维度。
Mathematical models that describe the tumor growth process have been formulated by several authors in order to understand how cancer develops and to develop new treatment approaches. In this study, it is aimed to investigate the long-time behavior of the two-phase diffuse-interface model, which was proposed in [11] to model a tumor tissue as a mixture of cancerous and healthy cells. Up to now, studies on the long-time behavior of this model have neglected chemotaxis and active transport, which have a significant effect on tumor growth. In this research, our main aim is to study this model with chemotaxis and active transport. We prove an asymptotic compactness result for the weak solutions of the problem in the whole phase-space $H^1 (Ω) \times L^2 (Ω)$. We establish the existence of the global attractor in a phase space denoted via mass conservation. We also prove that the global attractor equals to the unstable manifold emanating from the set of stationary points. Moreover, we obtain that the global attractor has a finite fractal dimension.
