Existence for a class of partial differential equations with nonlocal conditions
Existence for a class of partial differential equations with nonlocal conditions
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DOI：
10.1016/j.na.2008.04.009
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发表时间：
2009-05-01
影响因子：
1.4
通讯作者：
Chang, Jung-Chan
中科院分区：
文献类型：
--
作者：
Liu, Hsiang;Chang, Jung-Chan
研究非局部柯西问题的温和解和经典解的存在性。我们假设线性部分生成一个解析紧有界半群，而非线性部分是关于线性部分的分数阶幂范数的Holder连续函数。考虑到a-范数的非局部条件，我们推广了最近关于这一主题的结论。所得结果将应用于一类范数上具有非局部条件的泛函偏微分方程。(c) 2008 Elsevier Ltd.版权所有。
This paper is concerned with the existence of mild and classical solutions of nonlocal Cauchy problems. We assume that the linear part generates an analytic compact bounded semigroup, and that the nonlinear part is a Holder continuous function with respect to the fractional power norm of the linear part. Considering the nonlocal conditions in the a-norm, we generalize the recent conclusions on this topic. The results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in norm. (c) 2008 Elsevier Ltd. All rights reserved.