Affiliations: Departamento de Métodos Matemáticos, Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Rio de Janeiro, RJ, Brasil
Note: [] Correspondence to: J. da S. Ferreira, Departmento de Métodos Matemáticos, Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Rio de Janeiro, RJ, Brasil.
Note: [] This work was done while the author was visiting the Laboratoire d'Analyse Numérique of the Université Pierre et Marie Curie (Paris VI), sponsored by Conselho Nacional de Desenvolvimento Científico e Technológico - CNPq (Brasil). Proc. 20.2149/89.7.
Abstract: We study the exponential decay of the energy of the nonlinear system of Klein–Gordon equations utt−Δu+m1u+f(u,v)+a(x)ut=0, vtt−Δv+m2v+g(u,v)+b(x)vt=0,(x,t)∈O×(0,∞),u=v=0 on Γ0×(0,∞), where O is abounded or unbounded domain in RN with smooth boundary ro Γ0:=∂O;a,b∈L∞+O,a,b≥constant>0, a.e. in some appropriated open subset of O, and f, g satisfy some suitable conditions. The exponential decay of the energy is established by adapting to the system multiplier techniques of J.L. Lions, some techniques developed by E. Zuazua for a single equation and a unique continuation principle of A. Ruiz.
