Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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01 Jan 2002TL;DR: In this paper, the Hille-Yosida type theorems settle the question of well-posedness to a great extend, many perturbation and approximation results have been established, and for a large class of problems the asymptotic behaviour can be studied on the basis of spectral theory and transform methods.
Abstract: There is a striking difference between autonomous and non-autonomous linear evolution equations. Autonomous problems are well understood in the framework of strongly continuous operator semigroups and their generalizations. The Hille-Yosida type theorems settle the question of well-posedness to a great extend, many perturbation and approximation results have been established, and for a large class of problems the asymptotic behaviour can be studied on the basis of spectral theory and transform methods. In these and many other areas semigroup theory has reached a considerable degree of maturity, and its applications thrive in plenty of fields.
71 citations
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TL;DR: The main results are in Section 4 (see Theorem 21) and the illustrative example in the last section is given.
71 citations
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TL;DR: The stability and asymptotic behavior of solutions of an autonomous linear differential system x' =,4x are determined by the spectrum of the constant matrix A as discussed by the authors, which is the limiting system X' = Ax.
68 citations
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TL;DR: In this article, a new asymptotic method of attack on the connection problem around the point at infinity for Painleve transcendents of the first and second kind is developed.
68 citations