Evolution Semigroups and Product Formulas for Nonautonomous Cauchy Problems
Evolution Semigroups and Product Formulas for Nonautonomous Cauchy Problems
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DOI：
10.1002/(sici)1522-2616(200004)212:1
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发表时间：
2000-04
影响因子：
1
通讯作者：
G. Nickel
中科院分区：
文献类型：
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作者：
G. Nickel
In this paper, we study nonautonomous Cauchy problems (NCP) {u(t) = A(t)u(t)u(s) = x ∈ X for a family of linear operators (A(t))t∈I on some Banach space X by means of evolution semigroups. In particular, we characterize “stability” in the so called “hyperbolic case” on the level of evolution semigroups and derive a product formula for the solutions of (NCP). Moreover, in Section 4 we connect the “hyperbolic” and the “parabolic” case by showing, that integrals ∫tsA(τ) dτ always define generators. This yields another product formula.
