Existence of polynomial attractor for a class of extensible beams with nonlocal weak damping and critical nonlinearity
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DOI: 10.1002/mma.9941
Abstract: The goal of this paper is to study the long time behavior of the extensible beams equation with the nonlocal weak damping utt+Δ2u−m(‖∇u‖2)Δu+‖ut‖put+f(u)=h$$ {u}_{tt}+{\Delta}^2u-m\left({\left\Vert \nabla u\right\Vert}^2\right)\Delta u+{\left\Vert {u}_t\right\Vert}^p{u}_t+f(u)=h $$ . In the case of critical… read more here.
Keywords: extensible beams; amp; nonlinearity; nonlocal weak ... See more keywords
Long-Time Dynamics of Balakrishnan–Taylor Extensible Beams
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DOI: 10.1007/s10884-019-09766-x
Abstract: This paper is concerned with well-posedness and long-time dynamics for a class extensible beams with nonlocal Balakrishnan–Taylor and frictional damping. The related model describes vibrations in nonlinear extensible beams arising in connection with models of… read more here.
Keywords: long time; balakrishnan taylor; extensible beams; time dynamics ... See more keywords