scholarly journals Energy uniform decay rates for the semilinear wave equation with nonlinear localized damping and source terms of critical variable exponent

2021 ◽  
Vol 9 Proceeding (1) ◽  
pp. 26-32
Author(s):  
Abita Rahmoune
Keyword(s):  
Wave Equation ◽  
Variable Exponent ◽  
Decay Rates ◽  
Source Terms ◽  
Uniform Decay ◽  
Critical Variable ◽  
Semilinear Wave Equation ◽  
Localized Damping ◽  
Damping And Source Terms

scholarly journals On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms

2009 ◽  
Vol 2 (3) ◽  
pp. 583-608 ◽  
Author(s):  
Claudianor O. Alves ◽  
◽  
M. M. Cavalcanti ◽  
Valeria N. Domingos Cavalcanti ◽  
Mohammad A. Rammaha ◽  
...  
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Blow Up ◽  
Decay Rates ◽  
Nonlinear Wave Equations ◽  
Source Terms ◽  
Uniform Decay ◽  
Damping And Source Terms

scholarly journals On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms

2005 ◽  
Vol 2005 (3) ◽  
pp. 219-233 ◽  
Author(s):  
E. Cabanillas Lapa ◽  
Z. Huaringa Segura ◽  
F. Leon Barboza
Keyword(s):  
Wave Equation ◽  
Source Term ◽  
Strong Solutions ◽  
Global Solvability ◽  
Uniform Stability ◽  
Source Terms ◽  
Nonlinear Dissipation ◽  
Quasilinear Wave Equation ◽  
Localized Damping ◽  
Damping And Source Terms

We prove existence and uniform stability of strong solutions to a quasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity of the typeu″−M(∫Ω|∇u|2dx)Δu+a(x)g(u′)+f(u)=0,inΩ×]0,+∞[,u=0,onΓ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), inΩ.

Stabilization of the wave equation with a nonlinear delay term in the boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wassila Ghecham ◽  
Salah-Eddine Rebiai ◽  
Fatima Zohra Sidiali
Keyword(s):  
Wave Equation ◽  
Original Problem ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Decay Rates ◽  
Uniform Decay ◽  
Delay Term ◽  
Nonlinear Semigroup Theory ◽  
Nonlinear Boundary Feedback ◽  
Nonlinear Delay

Abstract A wave equation in a bounded and smooth domain of ℝ n {\mathbb{R}^{n}} with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation.

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