D. C. Pereira, Hoang-Ngan Nguyen, C. Raposo, C. Maranhão
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On the solutions for an extensible beam equation with internal damping and source terms
In this manuscript, we consider the nonlinear beam equation with internal damping and source term utt +Δu+M(|∇u|)(−Δu)+ut = |u|r−1u where r > 1 is a constant, M(s) is a continuous function on [0,+∞) . The global solutions are constructed by using the Faedo-Galerkin approximations, taking into account that the initial data is in appropriate set of stability created from the Nehari manifold. The asymptotic behavior is obtained by the Nakao method.
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