Joly, J. L.; Métivier, G.; Rauch, J. Focusing and absorption of nonlinear oscillations. (English) Zbl 0815.35071 Journ. Équ. Dériv. Partielles, St.-Jean-de-Monts 1993, No. 3, 11 p. (1993). The Cauchy problem for the dissipative wave equation \[ u_{tt} - \Delta u + u | u |^ p = 0, \quad t > 0, \quad x \in \mathbb{R}^ d \] with fast oscillating initial functions is considered. The problem is a passage of the fast oscillating wave through a focal point, where the wave amplitude is increasing that is predicted by the geometric optics method. The main result is as follows: The oscillations which may be present in the initial data do not survive a passage through the focus, if \((d-1)p \geq 2\). Reviewer: L.Kalyakin (Ufa) Cited in 1 Document MSC: 35L70 Second-order nonlinear hyperbolic equations 78A05 Geometric optics Keywords:fast oscillating initial functions; passage of the fast oscillating wave through a focal point PDFBibTeX XMLCite \textit{J. L. Joly} et al., Journ. Équ. Dériv. Partielles, St.-Jean-de-Monts 1993, No. 3, 11 p. (1993; Zbl 0815.35071) Full Text: Numdam EuDML