In this paper, we address an inverse problem of reconstructing a space-dependent semilinear coefficient in the tumor growth model described by a system of semilinear partial differential equations (PDEs) with Dirichlet boundary condition using boundary-type measurement. We establish a new higher order weighted Carleman estimate for the given system with the help of Dirichlet boundary conditions. By deriving a suitable regularity of solutions for this nonlinear system of PDEs and the new Carleman estimate, we prove Lipschitz-type stability for the tumor growth model.

中文翻译：

---

模拟肿瘤生长的 Cahn-Hilliard 类型系统的逆问题

在本文中，我们解决了重建肿瘤生长模型中空间相关半线性系数的逆问题，该模型由具有狄利克雷边界条件的半线性偏微分方程 (PDE) 系统描述，使用边界类型测量。我们在狄利克雷边界条件的帮助下为给定系统建立了一个新的高阶加权卡尔曼估计。通过为这种 PDE 的非线性系统和新的 Carleman 估计推导合适的解的规律性，我们证明了肿瘤生长模型的 Lipschitz 型稳定性。