| Abstract: |
| In this talk, we investigate the asymptotic dynamics of a thermoelastic plate of Green-Lindsay type, a model characterized by two relaxation times that exhibits finite-speed heat waves. Recently, the well-posedness and exponential stability of the homogeneous linear problem were established, although it remained an open question whether the domain of the semigroup generator is compactly embedded into the energy space. We address this challenge by studying the system in the presence of a nonlinear foundation. By overcoming the technical difficulties associated with the lack of compact embedding, we prove the existence of a finite-dimensional smooth global attractor for the associated dynamical system. |
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