A boundary value problem connected with response of semi-space to a short laser pulse (Q1390736)

Summary: A mixed boundary value problem for a fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse and belongs to generalized thermoelasticity is studied. The present paper contains a proof of the existence, uniqueness and continuous dependence of the solution on the datum, together with an effective method for numerical computation of a solution and the behaviour of solutions as \(t\to \infty\). This article is the last scientific contribution of Gaetano Fichera. The paper -- whose draft was found on Gaetano Fichera's desk after his untimely death -- was prepared for publication by O. A. Oleinik, with the collaboration of M. P. Colautti and transmitted to the Academia by his wife. The original text was in its final form with the only apparent exception of the last few lines and, in particular, of the proof of Theorem 6.III. But a short note added by O. A. Oleinik [ibid. 197-228 (reviewed below)] indicates how the theorem, which concludes the article, can be obtained by the same techniques developed by the author in the preceding sections of the paper.