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Global solutions for a nonlinear Kirchhoff type equation with viscosity

Lapa Eugenio Cabanillas

Opuscula Mathematica

2023

Vol. 43, no. 5

689--701

In this paper we consider the existence and asymptotic behavior of solutions of the following nonlinear Kirchhoff type problem [formula] where [formula]. If the initial energy is appropriately small, we derive the global existence theorem and its exponential decay.

Exponential decay of solutions to a class of fourth-order nonlinear hyperbolic equations modeling the oscillations of suspension bridges

Liu Yang, Yang Chao

Opuscula Mathematica

2022

Vol. 42, no. 2

239--255

This paper is concerned with a class of fourth-order nonlinear hyperbolic equations subject to free boundary conditions that can be used to describe the nonlinear dynamics of suspension bridges.

Global existence and exponential decay for a viscoelastic equation with not necessarily decreasing kernel

Alaeddine Draifia

Journal of Applied Analysis

2022

Vol. 28, nr 2

219--236

In this paper, we consider the nonlinear viscoelastic equation utt − Δu + t∫0h(t − s)Δu(s) ds + a(x)|ut|mut + |u|γu = 0 in a bounded domain with kernels not necessarily exponentially decaying to zero and we obtain an asymptotic stability result of global solutions.

Exponential decay of transient values in discrete-time positive nonlinear systems

Kaczorek Tadeusz, Ruszewski Andrzej

Archives of Control Sciences

2022

Vol. 32, No. 3

577--588

The exponential decay of transient values in discrete-time nonlinear standard and fractional orders systems with linear positive linear part and positive feedbacks is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. A procedure for computation of gains characterizing the class of nonlinear elements are given and illustrated on simple example.