肿瘤生长的相场模型解的性质
Solutions of a Phase-Field Model for Tumor Growth
摘要: 本文研究了无血管期肿瘤生长的相场模型。该模型耦合了营养物质浓度n的Allen-Cahn方程和序参数 的Cahn-Hilliard方程，描述了肿瘤生长所需营养物质的扩散过程和肿瘤的演变过程。在本文中，我证明了初边值问题弱解的存在性，一维情况下解的唯一性以及稳态解的存在性。
Abstract: In this paper, we study the solutions to an initial-boundary value problem for a phase-field model of tumor growth, which is the Allen-Cahn equation for the nutrient concentration n coupled with the Cahn-Hilliard equation for the order parameter  , and describes the diffusion process of nutrient and the evolution process of tumor. I prove the existence of weak solutions to the problem and the uniqueness of global solution in one dimension. Finally, the existence of stationary solutions is proved.
文章引用：孙李丹. 肿瘤生长的相场模型解的性质[J]. 理论数学, 2021, 11(6): 1230-1241. https://doi.org/10.12677/PM.2021.116136

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