Y. Ye : Existence and Asymptotic Behavior of Global Solutions for Some Nonlinear Petrovsky System, p. 389-398


The initial-boundary value problem for some nonlinear Petrovsky system with viscoelastic term in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set in $H_0^2(\Omega)$ and the decay of solution energy is established by applying a difference inequality due to M.Nakao.

Key Words: Initial-boundary value problem; Nonlinear Petrovsky system; Global solutions; Viscoelastic term.

2010 Mathematics Subject Classification: 35A05; 35B40; 35L05.