论文标题
具有退化迁移率的非局部相田间肿瘤模型的强度良好和逆鉴定问题
Strong well-posedness and inverse identification problem of a non-local phase field tumor model with degenerate mobilities
论文作者
论文摘要
我们扩展了以前在Frigeri等人中获得的弱体性结果。 （2017）关于Hawkins-Daarud等人提出的弥漫界面肿瘤模型的非本地变体。 （2012年）。该模型由一个非本地Cahn--Hilliard方程组成，具有退化的迁移率和相位场变量的奇异潜力，并耦合到营养浓度的反应扩散方程。我们证明了该模型的强大解决方案，并建立了一些高阶连续依赖估计，即使在两个空间维度的浓度依赖性迁移率都存在浓度依赖性迁移率。然后，我们将新的规律性结果应用于研究一个反问题，该问题在终端时识别测量的初始肿瘤分布。将Tikhonov正则化逆问题制定为最小化问题，我们确定了最小化器的存在，并得出了一阶必要的最佳条件。
We extend previous weak well-posedness results obtained in Frigeri et al. (2017) concerning a non-local variant of a diffuse interface tumor model proposed by Hawkins-Daarud et al. (2012). The model consists of a non-local Cahn--Hilliard equation with degenerate mobility and singular potential for the phase field variable, coupled to a reaction-diffusion equation for the concentration of a nutrient. We prove the existence of strong solutions to the model and establish some high order continuous dependence estimates, even in the presence of concentration-dependent mobilities for the nutrient variable in two spatial dimensions. Then, we apply the new regularity results to study an inverse problem identifying the initial tumor distribution from measurements at the terminal time. Formulating the Tikhonov regularised inverse problem as a constrained minimisation problem, we establish the existence of minimisers and derive first-order necessary optimality conditions.
