This analysis demonstrates global attractor existence and energy dynamics in a coupled PDE system, indicating potential for long-term predictive modeling.
We study a third-order-in-time strongly dissipative PDE system with coupled field interaction. Two coupling branches are analyzed: (i) a quasi-static elliptic (Poisson-type) branch and (ii) a fully dynamic field branch. Within a unified energy framework, we establish well-posedness via Galerkin approximation and compactness arguments, prove dissipativity through Lyapunov energy estimates or full energy identities, demonstrate the existence of absorbing sets, and establish asymptotic compactness using Aubin–Lions and spectral tail estimates. Consequently, the associated semiflow admits a compact global attractor. A spectral Galerkin numerical demonstration illustrates energy decay, mode stabilization, and long-time bounded dynamics.
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Norbert Ferenc Nagy (2026) studied this question.
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