Large-time asymptotic behavior of solutions of nonlinear wave equations perturbed from a stationary ground state

Publisher Website
Google Scholar
Abstract
Let uo(x) be a nontrivial solution of the equation on which minimizes the energy functional . Here Where is continuous function satisfying Shown that uo can be perturbed into a time-dependent solution of the evolution equationu which remains bounded in energy norm for all . If and f satisfies a slightly more restrictive growth condition at infinity, then these solutions tend to zero as . It is also shown, in case , that with f modified to accommodate complex solutions uo can be perturbed into a complex stading wavy. Thus, in some sense, the stationary ground state is unstable with regard to the evolution equation.

This publication has 7 references indexed in Scilit: