The asymptotic theory of global solutions for semilinear wave equations in three space dimensions (Q1767869)

The authors present uniform estimates of a solution to the Cauchy problem for the equation \(u_{tt}-\triangle u=\varepsilon f(u,\varepsilon ),\) \(t>0\), \(x\in \mathbb R^3.\) Using a fixed-point theorem, they deduce the existence of a global classical solution and its asymptotic decay for sufficiently small \(\varepsilon .\) Convergence of formal approximations to the solution is also proved.