Representation and approximation of solutions to semilinear Volterra equations with delay
Representation and approximation of solutions to semilinear Volterra equations with delay
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DOI：
10.1016/0022-0396(79)90060-3
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发表时间：
1979-05
影响因子：
2.4
通讯作者：
W. Fitzgibbon
中科院分区：
文献类型：
--
作者：
W. Fitzgibbon
本文利用Crandall和Pazy的一个定理给出了半线性沃尔泰拉方程x（t）（t）=W（t，τ）<$（0）+<$τtW（t，s）F（s，xs（<$））ds解的非线性发展算子的积积分表示，其中核W（t，s）是Banach空间X上的线性发展算子，I是[−r，0]或（−∞，0]形式的区间，F是R ×C（I，X）到X的非线性映射.抽象理论应用于偏泛函微分方程的例子。
In this paper we use a theorem of Crandall and Pazy to provide the product integral representation of the nonlinear evolution operator associated with solutions to the semilinear Volterra equation:x(ϑ)(t) =W(t,τ)ϑ(0) + ∝τtW(t,s)F(s,xs(ϑ))ds.Here the kernelW(t,s) is a linear evolution operator on a Banach spaceX;Iis an interval of the form [−r, 0] or (−∞, 0] andFis a nonlinear mapping ofR×C(I,X) intoX. The abstract theory is applied to examples of partial functional differential equations.