Characterization of a class of evolution operators generated by time-dependent subdifferentials
Characterization of a class of evolution operators generated by time-dependent subdifferentials
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由时间相关的次微分生成的一类演化算子的表征
DOI：
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发表时间：
1989
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通讯作者：
M. Kubo
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文献类型：
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作者：
M. Kubo
给定实Hilbert空间H上的一族真下半连续凸函数族{φt；0≤t≤T}，我们感兴趣的是下面的发展方程：U‘(T)+∂φt(u(T))⊃f(T)，0<；t<；T，其中u’=Du/dt，∂φt是次微分，f是给定函数.目的是建立一个关于{φt}与时间相关的充要条件，使得f为≡0的柯西问题存在唯一解u满足某种类型的能量不等式
Given a family {φ t ; 0≤t≤T} of proper lower-semicontinuous convex functions on a real Hilbert space H, we are interested in the following evolution equation: u'(t)+∂φ t (u(t))⊃f(t), 0<t<T, where u'=du/dt, ∂φ t is the subdifferential and f is a given function. The purpose is to establish a condition on time-dependence of {φ t } which is necessary and sufficient in order that the Cauchy problem with f≡0 admits a unique solution u satisfying a certain type of energy inequality