×

Large time behavior of solutions to nonlinear systems of Klein-Gordon equations. (English) Zbl 0656.35115

New results concerning asymptotic properties of a pair of interacting relativistic (scalar) fields modeled by a system of nonlinear Klein-Gordon equations, are presented. As a consequence of our analysis we have: a) the local energy associated with solutions with finite energy decays as \(t\to +\infty\); b) if we allow dissipation in our system then we give an elementary proof of the exponential decay as \(t\to +\infty\) of finite energy solutions; c) for higher order interaction”, global regular solutions of the nonlinear system decay (in \(L^{\infty}\)-norm) like \(O(t^{-3/2})\) as \(t\to +\infty\), provided the initial data at \(t=0\) is “sufficiently small”.

MSC:

35Q40 PDEs in connection with quantum mechanics
35L70 Second-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDFBibTeX XMLCite