标题： 非自治的右乘和左乘摄动与最大正则性 显示英文标题

标题： Non-autonomous right and left multiplicative perturbations and maximal regularity

摘要： 我们考虑非自治柯西问题 $u'(t) + B(t)A(t)u(t) + P(t)u(t) = f(t), u(0) = u_0$ 和 $u'(t) + A(t)B(t)u(t) + P(t)u(t) = f (t), u(0) = u_0$的最大正则性问题。 在两种情况下，时变算子 $A(t)$ 与一个共轭双线性形式族相关联，乘法左或右扰动 $B(t)$ 以及加法扰动 $P(t)$ 都是所考虑的希尔伯特空间上的有界算子族。 我们在形式和扰动的最小正则性假设下，证明了前面问题解的最大 $L_p$-正则性结果和其他正则性性质。 显示英文摘要

摘要： We consider the problem of maximal regularity for non-autonomous Cauchy problems $u'(t) + B(t)A(t)u(t) + P(t)u(t) = f(t), u(0) = u_0$ and $u'(t) + A(t)B(t)u(t) + P(t)u(t) = f (t), u(0) = u_0$. In both cases, the time dependent operators $A(t)$ are associated with a family of sesquilinear forms and the multiplicative left or right perturbations $B(t)$ as well as the additive perturbation $P(t)$ are families of bounded operators on the considered Hilbert space. We prove maximal $L_p$-regularity results and other regularity properties for the solutions of the previous problems under minimal regularity assumptions on the forms and perturbations.