论文标题
使用化学疗法和抗血管生成疗法的前列腺癌生长的相位场模型的长时间动力学
Long time dynamics of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects
论文作者
论文摘要
我们考虑了[2]中引入的化学疗法和抗血管生成治疗作用的前列腺癌生长的相位模型。它由描述肿瘤生长的相位方程组成，该肿瘤生长与肿瘤的通用养分相结合。附加方程式将前列腺特异性抗原（PSA）的浓度融合在一起，并遵守线性反应扩散方程。该系统以肿瘤变量的均匀Dirichlet边界条件完成，养分和PSA浓度的Neuman边界条件。在这里，我们研究了模型的长时间动力学。我们首先证明，初始值问题在合适的相空间上产生了强烈的连续半群，该空间在适当的相空间中接收全球吸引子。此外，我们还讨论了解决方案与单个固定态的收敛性，并在某些条件下在系数上获得收敛速率估计。
We consider a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects which is introduced in [2]. It is comprised of phase-field equation to describe tumor growth, which is coupled to a reaction-diffusion type equation for generic nutrient for the tumor. An additional equation couples the concentration of prostate-specific antigen (PSA) in the prostatic tissue and it obeys a linear reaction-diffusion equation. The system completes with homogeneous Dirichlet boundary conditions for the tumor variable and Neuman boundary condition for the nutrient and the concentration of PSA. Here we investigate the long time dynamics of the model. We first prove that the initial-boundary value problem generates a strongly continuous semigroup on a suitable phase space that admits the global attractor in a proper phase space. Moreover, we also discuss the convergence of a solution to a single stationary state and obtain a convergence rate estimate under some conditions on the coefficients.
