Finite-dimensional asymptotic behavior of some semilinear damped hyperbolic problems |
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Authors: | Eduard Feireisl |
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Institution: | 1. Institute of Mathematics ?SAV, ?itná 25, 115 67, Praha 1, Czech Republic
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Abstract: | We prove that the solution semigroup $$S_t \left {u_0 ,v_0 } \right] = \left {u(t),u_t (t)} \right]$$ generated by the evolutionary problem $$\left\{ P \right\}\left\{ \begin{gathered} u_{tt} + g(u_t ) + Lu + f(u) = 0, t \geqslant 0 \hfill \\ u(0) = u_0 , u_t (0) = \upsilon _0 \hfill \\ \end{gathered} \right.$$ possesses a global attractorA in the energy spaceE o=V×L 2(Ω). Moreover,A is contained in a finite-dimensional inertial setA attracting bounded subsets ofE 1=D(L)×V exponentially with growing time. |
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