Almost automorphic solutions of evolution equations
Almost automorphic solutions of evolution equations
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DOI：
10.1090/s0002-9939-04-07571-9
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发表时间：
2004-06
期刊：
影响因子：
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通讯作者：
T. Diagana;G. N’Guérékata;N. Minh
中科院分区：
文献类型：
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作者：
T. Diagana;G. N’Guérékata;N. Minh
研究了方程（*）u（t）= Au（t）+ f（t）的几乎自守温和解的存在性，其中A生成一个全纯半群，f是几乎自守函数.由于几乎自守函数可能不是一致连续的，我们引入了函数的一致谱的概念。通过对已有工作中关于有界一致连续解的交换算子和方法的改进，得到了（*）的几乎自守温和解存在的充分条件，这些条件是关于A的虚谱和f的一致谱的.
This paper is concerned with the existence of almost automorphic mild solutions to equations of the form (*) u(t) = Au(t) + f(t), where A generates a holomorphic semigroup and f is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to (*) in terms of the imaginary spectrum of A and the uniform spectrum of f.