论文标题
在一类Volterra Integro-Differention方程的最大规律性上
On the maximal regularity for a class of Volterra integro-differential equations
论文作者
论文摘要
我们提出了一种基于扰动理论的方法，以建立一类Integro-differention方程的最大$ l^p $ - 型号。当左移半群涉及此类方程式时，我们研究了伯格曼空间上的最大规律性，用于自主和非自治的界面方程。我们的方法基于对库奇问题，无限尺寸系统理论的整数分化方程的制定以及有关最大规律性扰动的最新结果（请参阅\ cite \ cite {ambodrha}）。考虑到由Dirichlet（或Neumann） - 拉普拉斯式驱动的热方程式应用。
We propose an approach based on perturbation theory to establish maximal $L^p$-regularity for a class of integro-differential equations. As the left shift semigroup is involved for such equations, we study maximal regularity on Bergman spaces for autonomous and non-autonomous integro-differential equations. Our method is based on the formulation of the integro-differential equations to a Cauchy problems, infinite dimensional systems theory and some recent results on the perturbation of maximal regularity (see \cite{AmBoDrHa}). Applications to heat equations driven by the Dirichlet (or Neumann)-Laplacian are considered.
