共查询到17条相似文献,搜索用时 109 毫秒
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本文通过引入若干Lipschitz对偶概念,将非线性Lipschitz算子半群对偶映射到Lipschitz对偶空间中,使其转化为线性算子半群。该线性算子半群被证明是一个C_0~*-半群,因而是某个C_0-半群的对偶半群。从而证明了,在等距意义下,一个非线性Lipschitz算子半群可以延拓为一个C_0-半群。基于这些结论,本文给出了一系列全新的非线性Lipschitz算子半群的表示公式。 相似文献
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论文研究非自反Banach空间中Hille-Yosida算子的非线性Lipschitz扰动.首先,证明Hille-Yosida算子的非线性Lipschitz扰动诱导的微分方程的温和解构成非线性指数有界Lipschitz半群;其次,证明非线性扰动半群保持原半群的直接范数连续性质.获得的结果是线性算子半群某些结论的非线性推广. 相似文献
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研究有界线性算子强连续半群在非线性Lipschitz扰动下的正则性质保持问题.具体地,我们证明:如果强连续半群是直接范数连续的,则非线性扰动半群是直接Lipschitz范数连续的.结论推广了线性算子半群的范数连续性质保持,丰富和完善了非线性算子半群的理论. 相似文献
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《数学的实践与认识》2015,(16)
研究非自反Banach空间中Hille-Yosida算子的非线性Lipschitz扰动半群的直接紧性保持问题.具体地,在非线性Lipschitz半群的框架下,利用外推空间理论,证明非线性扰动半群保持原半群的直接紧性质.获得的研究结果是线性算子半群相应结果的非线性推广. 相似文献
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Banach空间的Lipschitz对偶及其应用 总被引:3,自引:0,他引:3
本文引进Banach空间E的一个全新对偶空间概念—Lipschitz对偶空间,并证明:任何Banach空间的Lipschitz对偶空间是某个包含E的Banach空间的线性对偶空间,以所引进的新对偶空间为框架,本文定义了非线性Lipschitz算子的Lipshitz对偶算子,证明:任何非线性Lipschitz算子的Lipschitz对偶算子是有界线性算子.所获结果为推广线性算子理论到非线性情形(特别,运用线性算子理论研究非线性算子的特性)开辟了一条新的途径.作为例证,我们应用所建立的理论证明了若干新的非线性一致Lipschitz映象遍历收敛性定理. 相似文献
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彭济根 《应用泛函分析学报》2005,7(1):39-45
基于作者先前提出的Lipschitz对偶思想,对非线性Lipschitz算子半群引入了若干Lipschitz对偶概念,得到了一类非线性Lipschitz算子半群存在生成元的特征刻画.这一结果直接将关于C0-半群如下结论推广到了非线性情形:C0-半群具有有界生成元当且仅当它一致连续. 相似文献
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借助于广义算子半群和广义积分算子半群的关系,讨论广义算子半群的Perron型指数稳定性,研究了广义积分算子半群的渐近行为. 相似文献
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Gustaf Söderlind 《BIT Numerical Mathematics》1984,24(4):667-680
A generalization of the logarithmic norm to nonlinear operators, the Dahlquist constant is introduced as a useful tool for the estimation and analysis of error propagation in general nonlinear first-order ODE's. It is a counterpart to the Lipschitz constant which has similar applications to difference equations. While Lipschitz constants can also be used for ODE's, estimates based on the Dahlquist constant always give sharper results.The analogy between difference and differential equations is investigated, and some existence and uniqueness results for nonlinear (algebraic) equations are given. We finally apply the formalism to the implicit Euler method, deriving a rigorous global error bound for stiff nonlinear problems.Dedicated to my teacher and friend, Professor Germund Dahlquist, on the occasion of his 60th birthday. 相似文献
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本文定义了非线性算子的Lip数,它从数值上刻画了在强等价距离意义下非线性算子的最小Lipschitz常数.基于所引进的Lip数,我们证明了线性算子Neumann引理及扰动引理的非线性推广.我们也给出了Lip数的两个极有意义的估值定理. 相似文献
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The logarithmic norm. History and modern theory 总被引:1,自引:0,他引:1
Gustaf Söderlind 《BIT Numerical Mathematics》2006,46(3):631-652
In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05 相似文献
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Alberto Guzman 《Journal of Functional Analysis》1978,30(2):223-237
We characterize certain semigroups, in terms of growth properties, as fractional-power semigroups associated with special linear operators. Such a semigroup is holomorphic in a sector containing the positive reals. Its norm may grow as a negative power of distance from the origin, and may grow extremely rapidly with angular approach to the edges of the sector of definition. We show that a semigroup of this kind can be viewed as {exp(?w(?A)a)}, where A is an operator whose resolvent is defined, with polynomial growth, in a region asymptotic, in a special sense, to a half-plane. 相似文献
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非线性Lipschitz连续算子的定量性质(Ⅳ)──谱理论 总被引:6,自引:4,他引:6
本文将有界线性算子谱的定义及若干重要谱性质推广至非线性Lipschitz连续算子,并得到一些有意义的结果. 相似文献
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Yoshikazu Kobayashi Toshitaka Matsumoto Naoki Tanaka 《Journal of Mathematical Analysis and Applications》2007,330(2):1042-1067
In this paper we introduce the notion of semigroups of locally Lipschitz operators which provide us with mild solutions to the Cauchy problem for semilinear evolution equations, and characterize such semigroups of locally Lipschitz operators. This notion of the semigroups is derived from the well-posedness concept of the initial-boundary value problem for differential equations whose solution operators are not quasi-contractive even in a local sense but locally Lipschitz continuous with respect to their initial data. The result obtained is applied to the initial-boundary value problem for the complex Ginzburg–Landau equation. 相似文献