The initial boundary value problems for linear non-autonomous first-order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change with t. We study existence, uniqueness and maximal regularity of solutions in Sobolev spaces. In contrast to the previous results, we use only the continuity assumption on the operators in the main part of the equation.

中文翻译：

---

非自治发展方程初边值问题的可解性

研究了线性非自治一阶发展方程的初始边值问题。我们的假设提供了适用于许多情况的统一处理方法，在这些情况下，运算符的域可能随t改变。我们研究Sobolev空间中解的存在性，唯一性和最大正则性。与先前的结果相反，我们仅在方程的主要部分中对算子使用连续性假设。