Özet
In this thesis, we concern the long time behaviours of the one dimensional strongly
damped nonlinear wave equation
u_tt-u_txx-∂/∂x (|u_x |^(p-2) u_x )+f(u)=g(x) (1)
in bounded domain and the one dimensional strongly damped nonlinear wave equation
with localized damping term
u_tt-u_txx-u_xx-∂/∂x (|u_x |^(p-2) u_x )+a(x) u_t+f(u)=g(x) (2)
in unbounded domain. The thesis consists of four sections. In the first section, the
previous studies about the long time dynamics of the strongly damped wave equations
and the main purpose of the thesis are mentioned. Second section is devoted to the
main theorems and definitions. In the third section, we prove the well-posedness of the
initial boundary value problem for equation (1) and the existence of regular strong
global attractor in W_0^(1,p)(0,1)×L^2(0,1) for the semigroup generated by the problem.
In the fourth section, we obtain the well-posedness of the initial value problem for
equation (2) and the existence of weak local attractors in (W^(1,p)(R)∩H^1(R))×L^2(R) for the semigroup generated by the problem.
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