Journal Article10.1007/BF00251609
Asymptotic stability in viscoelasticity
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TL;DR: In this article, it was shown that the solutions of (1.1) are asymptotically stable provided that g(T) is a nonnegative, monotonic non-increasing and convex function such that
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Abstract: where p, c are positive constants and g(r is independent of x; u(x, t) has been assigned on [0, 1 ] x ( oo, 0]. In a recent paper [1] the author investigated the problem of asymptotic stability for a class of abstract integrodifferential equations in function space, and the results were then applied to viscoelasticity. It was established, for instance, that the solutions of (1.1) are asymptotically stable provided that g(T) is a nonnegative, monotonic non-increasing and convex function such that
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Citations
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References
Dynamical systems and stability
TL;DR: Topologies introduced on state space for differential equations to obtain dynamical systems were introduced in this article, where the state space was used to obtain the dynamical system topology of dynamical networks.
316
An invariance principle for compact processes
TL;DR: In this paper, the authors study invariance in the framework of the theory of processes, which is a direct generalization of the concept of a topological dynamical system.
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