NONLINEAR IMPULSIVE EVOLUTION EQUATIONS
NONLINEAR IMPULSIVE EVOLUTION EQUATIONS
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发表时间：
2004
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通讯作者：
James H. Liu
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作者：
James H. Liu
研究一类非线性脉冲演化方程u ' (t) = Au(t) + f(t, u(t)), 0 < t < T0, t = ti, u(0) = u0,∆u(ti) = Ii(u(ti)), i = 1,2，…， 0 < t1 < t2 <…< T0，在Banach空间X中，其中a是强连续半群的生成，∆u(ti) = u(t+i) - u(ti)，其中Ii是一些算子。与传统的初值问题u(0) = u0相比，脉冲条件可以用来模拟更多的物理现象。首先利用半群理论研究了温和解的存在唯一性，然后证明了如果f是连续可微的，则温和解产生经典解。AMS （MOS）学科分类：34G。
We study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive evolution equation u′(t) = Au(t) + f(t, u(t)), 0 < t < T0, t = ti, u(0) = u0, ∆u(ti) = Ii(u(ti)), i = 1, 2, ..., 0 < t1 < t2 < ... < T0, in a Banach space X, where A is the generator of a strongly continuous semigroup, ∆u(ti) = u(t+i ) − u(ti ), and Ii’s are some operators. The impulsive conditions can be used to model more physical phenomena than the traditional initial value problems u(0) = u0. We apply the semigroup theory to first study the existence and uniqueness of the mild solutions, and then show that the mild solutions give rise to classical solutions if f is continuously differentiable. AMS (MOS) Subject Classification : 34G.