Solvability and Maximal Regularity of Parabolic Evolution Equations with Coefficients Continuous in Time
Solvability and Maximal Regularity of Parabolic Evolution Equations with Coefficients Continuous in Time
复制标题
系数时间连续的抛物型演化方程的可解性和最大正则性
DOI：
10.1006/jmaa.2000.7247
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发表时间：
2001
影响因子：
1.3
通讯作者：
R. Schnaubelt
中科院分区：
文献类型：
--
作者：
J. Prüss;R. Schnaubelt
本文建立了抛物型发展方程u‘(T)n=A(T)u(T)n+f(T)的Lp型极大正则性，并利用算子和方法和发展半群的方法证明了抛物型发展方程u’(T)=Au(T)u(T)n+∈C([0，n T]，n B(D(A(0))，n X))的Lp型极大正则性.将结果应用于具有连续系数的抛物型偏微分方程组。
Abstract We establish maximal regularity of type Lp for a parabolic evolution equation u′(t) = A(t)u(t) + f(t) with A( · ) ∈ C([0, T], L (D(A(0)), X)) and construct the corresponding evolution family on the underlying Banach space X. Our proofs are based on the operator sum method and the use of evolution semigroups. The results are applied to parabolic partial differential equations with continuous coefficients.