Convergence of the Kato approximants for evolution equations involving functional perturbations
Convergence of the Kato approximants for evolution equations involving functional perturbations
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DOI：
10.1016/0022-0396(83)90041-4
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发表时间：
1983-03
影响因子：
2.4
通讯作者：
A. Kartsatos;M. Parrott
中科院分区：
文献类型：
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作者：
A. Kartsatos;M. Parrott
建立了非线性抽象泛函微分方程u′（t）+ A（t）u（t）= F（t，ut），u 0= φε C1（β − r，0 β，X），tε β 0，T β，（E）的唯一强解的存在性. X是一个具有一致凸对偶空间的Banach空间，且对t ∈ β 0，T β，A（t）是m-增生的，满足一个适用于偏微分方程的时间依赖条件.函数F满足Lipschitz条件。本文的新奇在于证明了（E）的解u（t）是序列un（t）的一致极限（当n→∞），其中函数un（t）是包含Yosida逼近的逼近方程的连续可微解.因此，一个简单的近似方案，现在可用于这样的方程，在平行的方法涉及使用非线性演化算子理论。
The existence of a unique strong solution of the nonlinear abstract functional differential equation u′(t)+ A (t) u (t)= F (t, u t), u 0= φεC 1 (¦− r, 0¦, X), tε¦ 0, T¦,(E) is established. X is a Banach space with uniformly convex dual space and, for tϵ¦ 0, T¦, A (t) is m-accretive and satisfies a time dependence condition suitable for applications to partial differential equations. The function F satisfies a Lipschitz condition. The novelty of the paper is that the solution u (t) of (E) is shown to be the uniform limit (as n→∞) of the sequence u n (t), where the functions u n (t) are continuously differentiate solutions of approximating equations involving the Yosida approximants. Thus, a straightforward approximation scheme is now available for such equations, in parallel with the approach involving the use of nonlinear evolution operator theory.