论文标题
Cahn-Hilliard-Brinkman肿瘤生长模型可能具有奇异的潜力
Cahn-Hilliard-Brinkman model for tumor growth with possibly singular potentials
论文作者
论文摘要
我们分析了由Cahn-Hilliard-Brinkman系统组成的肿瘤生长的相位场模型，该模型统治了肿瘤质量的演变，并与适用于营养素的化学物种的对流反应扩散方程相结合。本文的主要新颖性涉及讨论涵盖非线性潜力的所有有意义案例的系统的薄弱解决方案的讨论。特别是，常规，对数和双重障碍物的典型选择在我们的论文中承认。与先前与类似模型相关的结果相比，我们建议，而不是经典的无流量条件，这是Cahn-Hilliard-type方程中出现的化学电位的差异元边界条件。此外，假定可能取决于解决方案变量的源术语的抽象生长条件。
We analyze a phase field model for tumor growth consisting of a Cahn-Hilliard-Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diffusion equation for a chemical species acting as a nutrient. The main novelty of the paper concerns the discussion of the existence of weak solutions to the system covering all the meaningful cases for the nonlinear potentials; in particular,the typical choices given by the regular, the logarithmic, and the double obstacle potentials are admitted in our treatise. Compared to previous results related to similar models, we suggest, instead of the classical no-flux condition, a Dirichlet boundary condition for the chemical potential appearing in the Cahn-Hilliard-type equation. Besides, abstract growth conditions for the source terms that may depend on the solution variables are postulated.
