On finite fractal dimension of the global attractor for the wave equation with nonlinear damping
The author considers the following nonlinear wave equation \[ u_{tt}+g(u_t)-\Delta u + f(u) =0, \quad x\in \Omega,\;t>0, \] \[ u(x,t)=0, \quad x\in \partial \Omega,\;t>0, \] \[ u(x,0)=u_0(x),\;u_t(x,0)=u_1(x), \quad x\in \Omega. \] If \(f\) and \(g\) are smooth and satisfy some polynomial growth conditions, then the global attractor associated with this equation has a finite fractal dimension.
scientific article; zbMATH DE number 1879631