Cahn-Hillillard等式的相对能源估计值,其浓度依赖流动性 (Relative energy estimates for the Cahn-Hilliard equation with concentration dependent mobility)

Based on relative energy estimates, we study the stability of solutions to the Cahn-Hilliard equation with concentration dependent mobility with respect to perturbations. As a by-product of our analysis, we obtain a weak-strong uniqueness principle on the continuous level under realistic regularity assumptions on strong solutions. We then show that the stability estimates can be further inherited almost verbatim by appropriate Galerkin approximations in space and time. This allows us to derive sharp bounds for the discretization error in terms of certain projection errors and to establish order-optimal a-priori error estimates for semi- and fully discrete approximation schemes.

翻译：根据相对能源估计,我们研究卡恩-希利亚德等式的解决方案的稳定性,该等式的浓度取决于流动性,作为我们分析的副产品,我们根据现实的定期性假设,在强有力的解决方案下,在连续水平上获得一个弱强的独特性原则。然后,我们表明,稳定性估计数可以通过在空间和时间上适当的加勒金近似法进一步逐字传承。这使我们能够从某些预测错误中得出离散错误的清晰界限,并为半离散和完全离散的近似方案确定最优的顺序误差估计数。