论文标题
非自主进化方程的最大规律性
Maximal Regularity for Non-Autonomous Evolutionary Equations
论文作者
论文摘要
我们讨论了具有非自主系数的进化方程的最大规律性问题。此处进化方程是希尔伯特空间中考虑的抽象部分差异代数方程。捕获是考虑在指数加权的希尔伯特空间中考虑时间依赖的偏微分方程。顺便说一句，一个人将时间导数确定为一种连续的可逆，正常运算符，该算子允许具有光谱表示的傅立叶 - 宽段转换的功能性演算。在这里，主要结果是仅基于假定的方程式抛物线型结构和系数的托架型结构的规律性结果，并估计了时间派生剂的平方根。因此，我们同时将可用结果概括为非平滑域的文献。示例以差异形式，非自治和粗糙系数的扰动以及涡流类型的非自治方程。
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider time-dependent partial differential equations in an exponentially weighted Hilbert space. In passing, one establishes the time derivative as a continuously invertible, normal operator admitting a functional calculus with the Fourier--Laplace transformation providing the spectral representation. Here, the main result is then a regularity result for well-posed evolutionary equations solely based on an assumed parabolic-type structure of the equation and estimates of the commutator of the coefficients with the square root of the time derivative. We thus simultaneously generalise available results in the literature for non-smooth domains. Examples for equations in divergence form, integro-differential equations, perturbations with non-autonomous and rough coefficients as well as non-autonomous equations of eddy current type are considered.
