Displaying similar documents to “Local attractivity in nonautonomous semilinear evolution equations”

A characterization of evolution operators

Naoki Tanaka (2001)

Studia Mathematica

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A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.

Exponential stability of nonlinear non-autonomous multivariable systems

Michael I. Gil' (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady...

Banach function spaces and exponential instability of evolution families

Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu (2003)

Archivum Mathematicum

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In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families.

Permanence and global exponential stability of Nicholson-type delay systems

Zhonghuai Wu, Jianying Shao, Mingquan Yang, Wei Gao (2011)

Annales Polonici Mathematici

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We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].

Non-exponential and polynomial stability results of a Bresse system with one infinite memory in the vertical displacement

Aissa Guesmia (2017)

Nonautonomous Dynamical Systems

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The asymptotic stability of one-dimensional linear Bresse systems under infinite memories was obtained by Guesmia and Kafini [10] (three infinite memories), Guesmia and Kirane [11] (two infinite memories), Guesmia [9] (one infinite memory acting on the longitudinal displacement) and De Lima Santos et al. [6] (one infinite memory acting on the shear angle displacement). When the kernel functions have an exponential decay at infinity, the obtained stability estimates in these papers lead...

Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method

Abdoua Tchousso, Thibaut Besson, Cheng-Zhong Xu (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering...

On Exponential Stability of Volterra Difference Equations with Infinite Delay

Pham Huu Anh Ngoc, Le Trung Hieu (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.