HOMOGENIZATION RESULTS FOR A NONLINEAR WAVE EQUATION IN A PERFORATED DOMAIN

The effective behavior of the solution of a nonlinear wave equation in a periodic perforated domain is analyzed. We consider, at the microscale, a wave equation, with nonlinear sources and suitable initial and boundary conditions. We focus on the case in which the perforations are of the so-called critical size and we prove that the solution of this problem converges, as the small parameter characterizing the size of the holes tends to zero, to the solution of a new problem, containing extra zero order terms. Our paper generalizes some of the results contained in [3], by considering nonlinear sources.Original Abstract: Scopul acestei lucraari il constituie studiul comportamentului asimptotic al solutiei unei ecuatii a undelor intr-un mediu periodic perforat. Vom considera, la microscaraa, o ecuatie a undelor, cu surse neliniare si conditii initiale si la frontiera adecvate. Ne vom concentra atentia asupra cazului in care perforatiile au o dimensiune criticaa si vom demonstra caa solutia acestei probleme converge, cand parametrul mic ce caracterizeazaa maarimea perforatiilor tinde caatre zero, caatre solutia unei noi probleme, care contine termeni suplimentari. Rezultatele prezentate sunt generalizaa ale unor rezultate obtinute in [3], prin considerarea unor surse neliniare.