发表机构
Politecnico di Milano（米兰理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对带退化迁移率和奇异扩散的Cahn-Hilliard方程初边值问题，在三维有界光滑凸域且初始数据具有限能量的条件下，通过非熵方法推导关键函数的L⁴(0,T;H²(Ω))估计，证明了合适整体弱解的存在性。
AI 中文摘要
我们研究带有退化迁移率和纯相奇异扩散的Cahn-Hilliard方程的初边值问题，该模型描述了关联Flory-Huggins-de Gennes自由能的聚合物共混物中的相分离动力学。我们假设初始数据具有有限能量，证明了三维有界光滑凸域中合适整体弱解的存在性。本分析的一个关键创新点是，在不依赖经典基于熵的方法的情况下，得到了解u和函数φ(u)=arcsin(u)的L⁴(0,T;H²(Ω))估计。
英文摘要
We study the initial-boundary value problem for the Cahn-Hilliard equation with degenerate mobility and singular diffusion at pure phases. This model describes the dynamics of phase separation in polymer blends with associated Flory-Huggins-de Gennes free energy. We prove the existence of global weak solutions in three-dimensional bounded and smooth domains, assuming that the initial datum has finite energy. We show the classical regularity in $L^2(0,T;H^2(Ω))$ for both the solution $u$ and the function $ϕ(u)=\arcsin(u)$ through entropy estimates. In addition, when $Ω$ is convex, a new elliptic-type argument yields the refined regularity $u, ϕ(u) \in L^4(0,T; H^2(Ω))$.
CommentsCompared to the first version, the present manuscript replaces one of the two proofs of a main result, after a gap was identified in the original argument. Furthermore, the main result is extended to the setting of general bounded smooth domains
