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Global and exponential attractors for the singularly perturbed extensible beam

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  • The paper deals with the nonlinear evolution equation

    ε∂ttu + $\delta$∂tu+ $\omega$∂xxxx u-$[\beta+\int_0^1[\partial_y u(y,t)]^2\d y ]$∂xxu=f,

    which describes the motion of the vertical deflection of an extensible Kirchhoff beam. The existence of the global attractor of optimal regularity is shown, as well as the existence of a family of exponential attractors Hölder-continuous in the symmetric Hausdorff distance (with respect to ε) and of finite fractal dimension uniformly bounded with respect to ε.

    Mathematics Subject Classification: 35B25, 35B41, 35B65, 37B25, 74K05, 74K10.


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