Uniform decay rate estimates for the beam equation with locally distributed nonlinear damping

2021 ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Leonel G. Delatorre ◽  
Valéria N. Domingos Cavalcanti ◽  
Victor H. Gonzalez Martinez ◽  
Daiane C. Soares
Keyword(s):  
Decay Rate ◽  
Nonlinear Damping ◽  
Beam Equation ◽  
Uniform Decay

Global Existence and Uniform Decay of Solutions for a Kirchhoff Beam Equation with Nonlinear Damping and Source Term

2021 ◽  
Author(s):  
Ducival C. Pereira ◽  
Carlos A. Raposo ◽  
Celsa H. M. Maranhão ◽  
Adriano P. Cattai
Keyword(s):  
Global Existence ◽  
Source Term ◽  
Nonlinear Damping ◽  
Beam Equation ◽  
Uniform Decay ◽  
Decay Of Solutions

Uniform decay rate estimates for the coupled semilinear wave system in inhomogeneous media with locally distributed nonlinear damping

2020 ◽  
Vol 117 (1-2) ◽  
pp. 67-111
Author(s):  
A.F. Almeida ◽  
M.M. Cavalcanti ◽  
R.B. Gonzalez ◽  
V.H. Gonzalez Martinez ◽  
J.P. Zanchetta
Keyword(s):  
Decay Rate ◽  
Nonlinear Damping ◽  
Inhomogeneous Media ◽  
Wave System ◽  
Uniform Decay

Uniform decay rate estimates for the semilinear wave equation in inhomogeneous medium with locally distributed nonlinear damping

Nonlinearity ◽  
2018 ◽  
Vol 31 (9) ◽  
pp. 4031-4064 ◽  
Author(s):  
Marcelo M Cavalcanti ◽  
Valéria N Domingos Cavalcanti ◽  
Ryuichi Fukuoka ◽  
Ademir B Pampu ◽  
María Astudillo
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
Inhomogeneous Medium ◽  
Nonlinear Damping ◽  
Uniform Decay ◽  
Semilinear Wave Equation

Well-Posedness and Uniform Decay Rates for a Nonlinear Damped Schrödinger-Type Equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Valéria N. Domingos Cavalcanti
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Differential Operators ◽  
Type Equation ◽  
Nonlinear Damping ◽  
Decay Rates ◽  
Dirichlet Boundary Conditions ◽  
Uniform Decay ◽  
Pseudo Differential Operators ◽  
The One

Abstract In this paper we study the existence as well as uniform decay rates of the energy associated with the nonlinear damped Schrödinger equation, i ⁢ u t + Δ ⁢ u + | u | α ⁢ u - g ⁢ ( u t ) = 0   in  ⁢ Ω × ( 0 , ∞ ) , iu_{t}+\Delta u+|u|^{\alpha}u-g(u_{t})=0\quad\text{in }\Omega\times(0,\infty), subject to Dirichlet boundary conditions, where Ω ⊂ ℝ n {\Omega\subset\mathbb{R}^{n}} , n ≤ 3 {n\leq 3} , is a bounded domain with smooth boundary ∂ ⁡ Ω = Γ {\partial\Omega=\Gamma} and α = 2 , 3 {\alpha=2,3} . Our goal is to consider a different approach than the one used in [B. Dehman, P. Gérard and G. Lebeau, Stabilization and control for the nonlinear Schrödinger equation on a compact surface, Math. Z. 254 2006, 4, 729–749], so instead than using the properties of pseudo-differential operators introduced by cited authors, we consider a nonlinear damping, so that we remark that no growth assumptions on g ⁢ ( z ) {g(z)} are made near the origin.

scholarly journals General decay rate of a weakly dissipative viscoelastic equation with a general damping

2020 ◽  
Vol 40 (6) ◽  
pp. 647-666
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Wide Class ◽  
Nonlinear Damping ◽  
Numerical Results ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Viscoelastic Equation

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

scholarly journals On an extensible beam equation with nonlinear damping and source terms

2013 ◽  
Vol 254 (9) ◽  
pp. 3903-3927 ◽  
Author(s):  
Zhijian Yang
Keyword(s):  
Nonlinear Damping ◽  
Beam Equation ◽  
Source Terms ◽  
Damping And Source Terms

Uniform decay rates of coupled anisotropic elastodynamic/Maxwell equations with nonlinear damping

2011 ◽  
pp. 205-238
Author(s):  
Cleverson Roberto da Luz ◽  
Gustavo Alberto Perla Menzala
Keyword(s):  
Maxwell Equations ◽  
Nonlinear Damping ◽  
Decay Rates ◽  
Uniform Decay

scholarly journals Global existence and blow-up results for a nonlinear model for a dynamic suspension bridge

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Quang-Minh Tran ◽  
Hong-Danh Pham
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Decay Rate ◽  
Wave Equations ◽  
Source Term ◽  
Blow Up ◽  
Suspension Bridge ◽  
Nonlinear Damping ◽  
Damping Term ◽  
General Decay Rate

<p style='text-indent:20px;'>The paper deals with global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and superlinear source term with the coefficient depends on space and time variable. In the case the weak solution is global, we give information on the decay rate of the solution. In the case the weak solution blows up in finite time, estimate the lower bound and upper bound of the lifespan of the blow-up solution, and also estimate the blow-up rate. Finally, if our problem contains an external vertical load term, a sufficient condition is also established to obtain the global existence and general decay rate of weak solutions.</p>

scholarly journals Stochastic dynamic for an extensible beam equation with localized nonlinear damping and linear memory

2020 ◽  
Vol 4 (1) ◽  
pp. 400-416
Author(s):  
Abdelmajid Ali Dafallah ◽  
◽  
Fadlallah Mustafa Mosa ◽  
Mohamed Y. A. Bakhet ◽  
Eshag Mohamed Ahmed ◽  
...  
Keyword(s):  
Nonlinear Damping ◽  
Random Attractor ◽  
Beam Equation ◽  
Stochastic Dynamic ◽  
Uniqueness Of Solutions ◽  
Stochastic Dynamical System ◽  
Autonomous Case ◽  
Bounded Absorbing Set ◽  
Linear Damping ◽  
Longtime Behavior

In this paper, we concerned to prove the existence of a random attractor for the stochastic dynamical system generated by the extensible beam equation with localized non-linear damping and linear memory defined on bounded domain. First we investigate the existence and uniqueness of solutions, bounded absorbing set, then the asymptotic compactness. Longtime behavior of solutions is analyzed. In particular, in the non-autonomous case, the existence of a random attractor attractors for solutions is achieved.

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