an:01398353
Zbl 0939.35122
Haraux, Alain; Jendoubi, Mohamed Ali
Convergence of bounded weak solutions of the wave equation with dissipation and analytic nonlinearity
EN
Calc. Var. Partial Differ. Equ. 9, No. 2, 95-124 (1999).
00060030
1999
j
35L70 35B40 35L20
nonlinear wave equation with dissipation; compactness; boundedness
The paper deals with the initial boundary value problem for the equation \( u_{tt}+cu_{t}= \triangle u+f(x,u)\) in \(\mathbb{R}\times \Omega ,\) where \(\Omega \) is a bounded smooth domain in \(\mathbb{R}^{N}\), \(c\) is a positive constant, and \(f\) is an analytic (in \(u\)) function satisfying some growth conditions. The authors prove, that if the trajectory of a solution \(u\) is bounded in \(H^{0}_{1}(\Omega) \times L^{2}(\Omega),\) then \(u\) converges to a solution of the appropriate stationary problem. Some examples and some more general variants of the result are also given.
Marie Kop????kov?? (Praha)