scholarly journals Uniform Decay Rates of Solutions to a Nonlinear Wave Equation with Boundary Condition of Memory Type

2006 ◽  
pp. 239-255 ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Valéria N. Domingos Cavalcanti ◽  
Mauro L. Santos
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Decay Rates ◽  
Uniform Decay ◽  
Memory Type

scholarly journals On Existence, Uniform Decay Rates, and Blow-Up for Solutions of a Nonlinear Wave Equation with Dissipative and Source

2012 ◽  
Vol 2012 ◽  
pp. 1-27
Author(s):  
Xiaopan Liu
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Nonlinear Wave Equation ◽  
Energy Method ◽  
Blow Up ◽  
Existence Of Solution ◽  
Decay Rates ◽  
Nonlinear Hyperbolic Equation ◽  
Asymptotic Behaviors ◽  
Uniform Decay

This paper studies the blow-up and existence, and asymptotic behaviors of the solution of a nonlinear hyperbolic equation with dissipative and source terms. By using Galerkin procedure and the perturbed energy method, the local and global existence of solution is established. In addition, by the concave method, the blow-up of solutions can be obtained.

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.

On the global existence and asymptotic behavior of the solution of a nonlinear wave equation with past history

2021 ◽  
Vol 62 (3) ◽  
pp. 031512
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Mohammad Kafini ◽  
Shadi Al-Omari
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Past History
Sign in / Sign up

Export Citation Format

Share Document