| AN EXPONENTIAL STABILITY PROBLEM ON THE SMALL DELAY LINEAR SYSTEM |
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| 作者姓名： | 宋国柱 沈隽皓 |
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| 作者单位： | Department of Mathematics，Nanjing University，Nanjing 210008，China |
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| 摘 要： | 1IntroductionLetXbea'Banachspace,andB(X)betheBanachspaceofcontinuouslinearoperatorsfromXintoX.LetT(t)bea(CO)selltigroup,andletAbeitsinfinitesilllalgenerator.WedenotethedomainandtherangeofAbyD(A)andR(A).LetBbelongtoB(X).FOrthelinearsystem:andthedelaylinearsystem:wherer>0,((.)EC(--.,o],x)={fif:--r,oj~X,fiscontinuous},r(t)ECo,.)'05r(t)5r.Weconsidertileexponentialstabilityequivalencebetweellthesolutionof(1)and(2),whichllleans:ifthereexistM,a>0,sllththatIIS(f)II5Me--"'(f20),whereS(…
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AN EXPONENTIAL STABILITY PROBLEM ON THE SMALL DELAY LINEAR SYSTEM |
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| Song Guozhu,Shen Junhao.AN EXPONENTIAL STABILITY PROBLEM ON THE SMALL DELAY LINEAR SYSTEM[J].Acta Mathematica Scientia,1997(4). |
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| Authors: | Song Guozhu Shen Junhao |
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| Abstract: | In this paper, we define the mild solution of the delay system, and consider the eristence and uniqueness of the mild solution of the delay system. The relationship between the solution of linear system and the one of the delay system will be considered.And we also discuss the exponential stability equivalence between the solution of the linear system and the mild solution of the delay system. |
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| Keywords: | Delay system (C_0) semigroup (1 A) semigroup Exponential stability |
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