Global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains

2009 ◽  
Vol 29 (5) ◽  
pp. 1203-1215
Author(s):  
Bae Jeong Ja
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Exterior Domains ◽  
Nonlinear Dissipation ◽  
Quasilinear Wave Equation ◽  
Weakly Nonlinear

scholarly journals Global existence and energy decay of solutions to the Cauchy problem for a wave equation with a weakly nonlinear dissipation

2004 ◽  
Vol 2004 (11) ◽  
pp. 935-955 ◽  
Author(s):  
Abbès Benaissa ◽  
Soufiane Mokeddem
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Global Existence ◽  
Stable Set ◽  
Nonlinear Dissipation ◽  
Weakly Nonlinear ◽  
Dissipative Term ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
The Cauchy Problem

We prove the global existence and study decay properties of the solutions to the wave equation with a weak nonlinear dissipative term by constructing a stable set inH1(ℝn).

On a quasilinear wave equation with nonlinear damping

1988 ◽  
Vol 110 (3-4) ◽  
pp. 227-239 ◽  
Author(s):  
Dang Dinh Hai
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Nonlinear Damping ◽  
Quasilinear Wave Equation ◽  
Uniqueness Of The Solution ◽  
Global Existence And Uniqueness ◽  
Image Position

SynopsisWe prove the global existence and uniqueness of the solution of the initial and boundary value problem for the equationby using the classical Galerkin method when the forcing term and the initial data are in some sense small. The asymptotic behaviour of the solution as t → ∞ is also considered.

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.

scholarly journals Global Existence for a Quasilinear Wave Equation Outside of Star-Shaped Domains

2002 ◽  
Vol 189 (1) ◽  
pp. 155-226 ◽  
Author(s):  
Markus Keel ◽  
Hart F. Smith ◽  
Christopher D. Sogge
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Quasilinear Wave Equation
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