Abstract
The longtime behavior of a kind of fully magnetic effected nonlinear multi-dimensional piezoelectric beam with viscoelastic infinite memory is considered. The well-posedness of this nonlinear coupled PDEs’ system is showed by means of the semigroup theories and Banach fixed-point theorem. Based on frequency-domain analysis, it is proved that the corresponding coupled linear system can be indirectly stabilized exponentially by only one viscoelastic infinite memory term, which is located on one equation of these strongly coupled PDEs. Then, the exponential decay of the solution to the nonlinear coupled PDEs’ system is established by the energy estimation method under certain conditions.
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