Finite-dimensional asymptotic behavior of some semilinear damped hyperbolic problems

  • Eduard Feireisl
Article

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 spaceEo=V×L2(Ω). Moreover,A is contained in a finite-dimensional inertial setA attracting bounded subsets ofE1=D(LV exponentially with growing time.

Key words

Semilinear hyperbolic equation attractor asymptotic behavior 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Eduard Feireisl
    • 1
  1. 1.Institute of Mathematics čSAVPraha 1Czech Republic

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