Journal ArticleDOI
General decay for a viscoelastic equation of variable coefficients with a time-varying delay in the boundary feedback and acoustic boundary conditions
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In this paper, a variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered, and general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions.About:
This article is published in Acta Mathematica Scientia.The article was published on 2017-09-01. It has received 11 citations till now. The article focuses on the topics: Mixed boundary condition & Robin boundary condition.read more
Citations
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On a Multi-Delay Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion
TL;DR: In this paper, a class of multi-delay predator-prey model with feedback controls and prey diffusion is studied and sufficient conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using fixed point theory and some new analysis techniques.
Journal ArticleDOI
Optimal decay for second-order abstract viscoelastic equation in Hilbert spaces with infinite memory and time delay
Houria Chellaoua,Yamna Boukhatem +1 more
Journal ArticleDOI
Stability results for second-order abstract viscoelastic equation in Hilbert spaces with time-varying delay
Houria Chellaoua,Yamna Boukhatem +1 more
TL;DR: In this paper, a second-order abstract viscoelastic equation in Hilbert spaces with time-varying delay and a very general class of memory kernel functions is considered.
Journal ArticleDOI
Blow-up result for an abstract evolution problem with infinite memory and time-varying delay
Houria Chellaoua,Yamna Boukhatem +1 more
TL;DR: In this article, an abstract second-order viscoelastic equation with infinite memory, time-varying delay and a nonlinear source term is considered, and to the best of our knowledge, there is no blow-up res...
Posted Content
The wave equation with acoustic boundary conditions on non-locally reacting surfaces
Delio Mugnolo,Enzo Vitillaro +1 more
TL;DR: In this paper, the authors studied the well-posedness in the natural energy space and gave precise qualitative results for solutions when ε is bounded and ε r = 2, and the integral condition ε u_t=c^2 √int_{\Gamma_1}v.
References
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Journal ArticleDOI
Existence of a Solution of the Wave Equation with Nonlinear Damping and Source Terms
TL;DR: In this article, the authors studied the nonlinear wave equation involving the damping term u t | u t| m −1 and a source term of type u | u | p −1.
Journal ArticleDOI
Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks
Serge Nicaise,Cristina Pignotti +1 more
TL;DR: This paper considers the wave equation with a delayed velocity term and mixed Dirichlet-Neumann boundary condition and proves exponential stability of the solution under suitable assumptions.
Journal ArticleDOI
An example on the effect of time delays in boundary feedback stabilization of wave equations
TL;DR: In this article, the erect of time delays in boundary feedback stabilization schemes for wave equations is studied and the question is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays.
Proceedings ArticleDOI
Delayed Positive Feedback Can Stabilize Oscillatory Systems
TL;DR: In this article, a closed-loop system with positive, delayed feedback was shown to be stable for a range of delays using the Nyquist criterion, which is similar to the method proposed in this paper.
Journal ArticleDOI
Stabilization of wave systems with input delay in the boundary control
TL;DR: In this paper, the authors considered a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight (1 � µ) is applied over the other end.
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