论文标题
在具有质量来源的Cahn-Hilliard-Darcy系统上
On the Cahn-Hilliard-Darcy system with mass source and strongly separating potential
论文作者
论文摘要
我们研究了Cahn-Hilliard-Darcy类型的进化系统，包括质量来源和运输效应。该系统可能在与对流相关的许多物理情况下出现，主要和最特定的应用与肿瘤过程有关，其中质量的变化可能与肿瘤的生长或收缩相对应。在订单参数$φ$的配置潜力以这种方式设计的情况下，我们证明存在弱解决方案，尽管发生了质量源效应，但以这种方式将$φ$保持在参考间隔$（-1,1）$之间。此外，在二维情况下，我们获得了强（即更规则）解决方案的存在和独特性。
We study an evolutionary system of Cahn-Hilliard-Darcy type including mass source and transport effects. The system may arise in a number of physical situations related to phase separation phenomena with convection, with the main and most specific application being related to tumoral processes, where the variations of the mass may correspond to growth, or shrinking, of the tumor. We prove existence of weak solutions in the case when the configuration potential for the order parameter $φ$ is designed in such a way to keep $φ$ in between the reference interval $(-1,1)$ despite the occurrence of mass source effects. Moreover, in the two-dimensional case, we obtain existence and uniqueness of strong (i.e., more regular) solutions.
