Asymptotic behavior of solution to nonlinear evolution equations with damping

The same problem was studied by Tang and Zhao [S.Q. Tang, H.J. Zhao, Nonlinear stability for dissipative nonlinear evolution equations with ellipticity, J. Math. Anal. Appl. 233 (1999) 336-358], Nishihara [K. Nishihara, Asymptotic profile of solutions to nonlinear dissipative evolution system with ellipticity, Z. Angew. Math. Phys. 57 (4) (2006) 604-614] for the case of (ψ±,θ±)=(0,0).