Global existence of solutions to a wave equation with damping and source terms
This paper deals with the following mixed problem: \[ \begin{cases} u''-\Delta u+g(u')= |u|^{q-1} u\quad & \text{in }\Omega \times\mathbb{R}_+,\\ u=0 \quad & \text{on } \Gamma\times\mathbb{R}_+,\\ u(x,0)=u_0(x),\;u'(x,0)=u_1(x)\quad & \text{in } \Omega,\end{cases} \tag{1} \] where \(\Omega\subset \mathbb{R}^n\) is a bounded domain with smooth boundary \(\Gamma=\partial \Omega\) and \(g\) is a real-valued function. The author proves global existence of solution for (1) and studies the asymptotic behaviour of solution to (1) when \(g\) does not necessarily have polynomial growth near zero.
non-polynomial growth of the nonlinearity
scientific article; zbMATH DE number 1832869