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Existence and uniform decay for the Euler-Bernoulli viscoelastic equation with nonlocal boundary dissipation

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  • The linear Euler-Bernoulli viscoelastic equation

    $u_{t t} +\Delta^2 u-\int_0^t g(t-\tau) \Delta^2 u(\tau)d\tau = 0\quad$ in $\Omega \times (0,\infty)$

    subject to nonlinear boundary conditions is considered. We prove existence and uniform decay rates of the energy by assuming a nonlinear and nonlocal feedback acting on the boundary and provided that the kernel of the memory decays exponentially.

    Mathematics Subject Classification: 74K20, 74D10, 34B15, 93D20.


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