Autonomous nonlinear functional differential equations and nonlinear semigroups
Autonomous nonlinear functional differential equations and nonlinear semigroups
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DOI：
10.1016/0022-247x(74)90277-7
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发表时间：
1974-04
影响因子：
1.3
通讯作者：
G. Webb
中科院分区：
文献类型：
--
作者：
G. Webb
我们的目标是研究自治非线性泛函微分方程%(4)= d,+ a (4= we)), t> 0,（1.1）作为非线性算子半群的解。（1.1）中的符号遵循Hale[4]，即4 EC= C ([-Y, 01； KY)， Y> 0, F: C+[w ' ' （F可能是非线性的），~(4)(t):[-Y, co)+ IFP，对于t> 0,~~(4)是C的元素，对于每个0 E [-Y， 01]，由~~(4)(0)= a (+)（t+ 0）定义。在F为线性的情况下，（1.1）与线性算子半群理论的联系得到了广泛的发展（如Hale[4]）。我们的努力将首先是发展类似于线性情况的基本结果。我们将特别注意无穷小发生器的存在性和性质。然后，我们将使用半群集来处理(1)的数值近似。I)有限差分法。
Our objective is to study the solutions to the autonomous nonlinear functional differential equation%(4)= d,+ a (4= we)), t> 0,(1.1) as a semigroup of nonlinear operators. The notation in (1.1) follows Hale [4], ie, 4 EC= C ([-Y, 01; KY), Y> 0, F: C+[w”(F possibly nonlinear),~(4)(t):[-Y, co)+ IFP, and for t> 0,~~(4) is the element of C defined by~~(4)(0)= a (+)(t+ 0) for each 0 E [-Y, 01. In the case that F is linear, the connection of (1.1) to linear operator semigroup theory is extensively developed (eg, Hale [4]). Our efforts will first be to develop basic results analogous to the linear case. We shall give particular attention to the existence and properties of the infinitesimal generator. We shall then use the semigroup setting to treat the numerical approximation of (1. I) by means of finite difference methods.