July  2002, 8(3): 675-695. doi: 10.3934/dcds.2002.8.675

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

1. 

Departamento de Matemática - Universidade Estadual de Maringá, 87020-900 Maringá - PR, Brazil

Received  June 2001 Revised  October 2001 Published  April 2002

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.

Citation: Marcelo Moreira Cavalcanti. Existence and uniform decay for the Euler-Bernoulli viscoelastic equation with nonlocal boundary dissipation. Discrete & Continuous Dynamical Systems - A, 2002, 8 (3) : 675-695. doi: 10.3934/dcds.2002.8.675
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