Piecewise multiplier method and nonlinear integral inequalities for Petrowsky equation with nonlinear dissipation
The author proves that the piecewise multiplier method introduced by \textit{K. Liu} [SIAM J. Control Optimization 35, 1574--1590 (1997; Zbl 0891.93016)] and \textit{P. Martinez} [Rev. Mat. Complut. 12, 251--283 (1999; Zbl 0940.35034)] for the wave equation can be extended to the Petrowsky equation. Some recent results of the author are also applied in order to obtain decay rate estimates for the energy, without specifying the growth of the nonlinear dissipation close to the origin by means of convex properties and nonlinear integral inequalities for the energy of the solutions.
scientific article; zbMATH DE number 5118017