Nonlinear semigroups and the existence and stability of solutionsof semilinear nonautonomous evolution equations
Nonlinear semigroups and the existence and stability of solutionsof semilinear nonautonomous evolution equations
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非线性半群与半线性非自治演化方程解的存在性和稳定性
DOI：
10.1155/s108533759600019x
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发表时间：
1996
影响因子：
--
通讯作者：
N. Minh
中科院分区：
文献类型：
--
作者：
B. Aulbach;N. Minh
研究了一类半线性非自治演化方程解的存在性和稳定性。讨论了将所谓的演化半群（可能是非线性的）算子关联到每个非自治方程的过程。利用相应的无穷小发生器的吸积性给出了解的存在性、稳定性和周期振荡的存在性的充分条件。此外，通过抽象演化过程的积分流形的存在性，我们得到了温和解稳定性问题的约简原理。将所得结果应用于一类偏泛函微分方程。
This paper is concerned with the existence and stability of solutions of a class of semilinear nonautonomous evolution equations. A procedure is discussed which associates to each nonautonomous equation the so-called evolution semigroup of (possibly nonlinear) operators. Sufficient conditions for the existence and stability of solutions and the existence of periodic oscillations are given in terms of the accretiveness of the corresponding infinitesimal generator. Furthermore, through the existence of integral manifolds for abstract evolutionary processes we obtain a reduction principle for stability questions of mild solutions. The results are applied to a class of partial functional differential equations.