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ON THE SPECTRAL CHARACTERIZATION OF A STRONGLY CONTINUOUS PERTURBED SEMIGROUP
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作者 王海燕 阳名珠 《Acta Mathematica Scientia》 SCIE CSCD 1995年第S1期64-69,共6页
In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigro... In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigroup don't increase under the A-smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of the spectrum of generator and semgroup. 展开更多
关键词 strongly continuous semigroup Spectral mapping theorem Essential type.
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Rothe’s Fixed Point Theorem and the Controllability of the Benjamin-Bona-Mahony Equation with Impulses and Delay
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作者 Hugo Leiva Jose L. Sanchez 《Applied Mathematics》 2016年第15期1748-1764,共18页
For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbation... For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions. 展开更多
关键词 Interior Approximate Controllability Benjamin Bona-Mohany Equation with Impulses and Delay strongly continuous semigroup Rothe’s Fixed Point Theorem
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