Abstract
We study a nonlinear Cauchy problem modeling the motion of an extensible beam
in a bounded domain of \(\mathbb {R}^N\), with clamped boundary conditions in either cases: when \(r=\gamma =0\) or else when r and \(\gamma \) are positive. We prove, in both cases, the existence of solutions and the exponential decay of energy.
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This work is supported by Researchers Supporting Project number (RSPD2024R736), King Saud University, Riyadh, Saudi Arabia.
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Communicated by Abdelaziz Rhandi.
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Hajjej, Z. Exponential stability of extensible beams equation with Balakrishnan–Taylor, strong and localized nonlinear damping. Semigroup Forum 108, 391–412 (2024). https://doi.org/10.1007/s00233-024-10419-9
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DOI: https://doi.org/10.1007/s00233-024-10419-9