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A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse

Gaetano Fichera (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper a mixed boundary value problem for the 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. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective...

Addition to the Fichera paper

OLGA A. OLEINIK (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Asymptotic stability for a nonlinear evolution equation

Zhang Hongwei, Chen Guowang (2004)

Commentationes Mathematicae Universitatis Carolinae

We establish the asymptotic stability of solutions of the mixed problem for the nonlinear evolution equation ( | u t | r - 2 u t ) t - Δ u t t - Δ u - δ Δ u t = f ( u ) .

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