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

Refined estimates of the blow-up profile for a strongly perturbed semilinear wave equations in one space dimension