Asymptotic behavior of solutions to a class of fourth order nonlinear evolution equations with dispersive and dissipative terms
We study the long time asymptotic behavior of solutions to a class of fourth order nonlinear evolution equations with dispersive and dissipative terms. By using the integral estimation method combined with the Gronwall inequality, we point out that the global strong solutions of the problems decay to zero exponentially with the passage of time to infinity. The proof is rigorous and only based on some relatively weak assumptions on the nonlinear term.