Asymptotic behavior of solutions for initial-boundary value problems for strongly damped nonlinear wave equations
The initial-boundary value problem to the equation \(u_{tt}-a\Delta u_{t}-\Delta u+f(u)=0,\) where \(t>0,x\in \Omega \subset \mathbb R^n (n\geq 4),a>0,\) is studied. Under some conditions on \(f\) and \(a\) the authors prove that a global strong solution to this problem decays exponentially as \(t\rightarrow \infty .\)
scientific article; zbMATH DE number 5354998