Asymptotic behavior of the solutions of a nonlinear system of Klein-Gordon equations

Ferreira, José da Silva

doi:10.1016/0362-546x(89)90098-9

Cited by 8 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [16] Ferreira deduce decay results for the solutions of the system of nonlinear Klein-Gordon equations in R 3 , more precisely, if the inital datas are taken in C ∞ 0 (R 3 ) then, every solution of the system decays uniformly in x at the rate O(t − 3 2 ) as |t| → ∞, and is asymptotic to a free solution at t = ∞ or t = −∞. To get these results, they use techniques developed by Morawetz and Strauss.…”

Section: Remarkmentioning

confidence: 99%

Uniform stabilization of the Klein-Gordon system

Cavalcanti¹,

Delatorre²,

Soares³

et al. 2020

Communications on Pure &Amp; Applied Analysis

View full text Add to dashboard Cite

We consider the Klein-Gordon system posed in an inhomogeneous medium Ω with smooth boundary ∂Ω subject to two localized dampings. The first one is of the type viscoelastic and is distributed around a neighborhood ω of the boundary according to the Geometric Control Condition. The second one is a frictional damping and we consider it hurting the geometric condition of control. We show that the energy of the system goes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase-space. For this purpose, refined microlocal analysis arguments are considered by exploiting ideas due to Burq and Gérard [5]. Although the present problem has some similarity to the reference [6] it is important to mention that due to the Kelvin-Voigt dissipation character associated with the nonlinearity of the problem the approach used is completely new, which is the main purpose of this paper.

show abstract

Section: Remarkmentioning

confidence: 99%