scholarly journals On the pointwise decay estimate for the wave equation with compactly supported forcing term

2015 ◽  
Vol 14 (4) ◽  
pp. 1469-1480
Author(s):  
Hideo Kubo ◽  
Keyword(s):  
Wave Equation ◽  
Decay Estimate ◽  
Forcing Term ◽  
Compactly Supported ◽  
Pointwise Decay

scholarly journals Global existence for equivalent nonlinear special scale invariant damped wave equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sandra Lucente
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Vector Fields ◽  
Wave Equations ◽  
Small Data ◽  
Damped Wave Equation ◽  
Scale Invariant ◽  
Forcing Term ◽  
Time Existence

<p style='text-indent:20px;'>In this paper we give the notion of equivalent damped wave equations. As an application we study global in time existence for the solution of special scale invariant damped wave equation with small data. To gain such results, without radial assumption, we deal with Klainerman vector fields. In particular we can treat some potential behind the forcing term.</p>

scholarly journals PULLBACK AND FORWARD ATTRACTORS FOR A DAMPED WAVE EQUATION WITH DELAYS

2004 ◽  
Vol 04 (03) ◽  
pp. 405-423 ◽  
Author(s):  
T. CARABALLO ◽  
P. E. KLOEDEN ◽  
J. REAL
Keyword(s):  
Wave Equation ◽  
Compact Set ◽  
Damped Wave Equation ◽  
Forcing Term ◽  
Forward Attractor ◽  
Two Parameter

The existence of a pullback (and also a uniform forward) attractor is proved for a damped wave equation containing a delay forcing term which, in particular, covers the models of sine–Gordon type. The result follows from the existence of a compact set which is uniformly attracting for the two-parameter semigroup associated to the model.

scholarly journals A Decay Estimate for a Wave Equation with Trapping and a Complex Potential

2012 ◽  
Vol 2013 (3) ◽  
pp. 548-561 ◽  
Author(s):  
Lars Andersson ◽  
Pieter Blue ◽  
Jean-Philippe Nicolas
Keyword(s):  
Wave Equation ◽  
Complex Potential ◽  
Decay Estimate

scholarly journals The Rate at Which the Energy of Solutions for a Class ofp-Laplacian Wave Equation Decays

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Soufiane Mokeddem ◽  
Khaled Ben Walid Mansour
Keyword(s):  
Wave Equation ◽  
Weight Function ◽  
Decay Estimate ◽  
Global Solutions ◽  
Positive Function ◽  
Integral Inequalities ◽  
Multiplier Method ◽  
Special Weight

We will investigate the decay estimate of the energy of the global solutions to thep-Laplacian wave equation with dissipation of the formutt-div (∇xup-2∇xu)+σ(t)(ut-div (∇xutm-2∇xut))=0under suitable assumptions on the positive functionσ. For this end we use the multiplier method combined with nonlinear integral inequalities given by Martinez; the proof is based on the construction of a special weight function that depends on the behavior ofσ.

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