  We consider in this paper a class of strongly perturbed semilinear wave
equations with a non-characteristic point in one space dimension, for general
initial data. Working in the framework of similarity variables, in \cite {MZ}
Merle and Zaag constructed an explicit stationary solution of the unperturbed
problem and proved an exponential convergence to this family of solutions. If
we follow the same strategy under our strongly perturbed equation we just
obtain a polynomial convergence which is a rough estimate compared to the one
obtained in the unperturbed problem. In order to refine this approximation, we
constructed an implicit solution to the perturbed problem which approaches the
stationary solutions of the unperturbed problem and we prove the exponential
convergence to this prescribed blow-up profile.
