Analysis reveals weak solutions exhibit exponential decay in energy, indicating uniformly stable behavior of Kirchhoff-type plates.
This paper deals with initial-boundary value problems for a thin quasilinear plate equation. It is shown the global existence of weak and strong solutions, that the energy of the weak solution has an exponential decay rate, and the strong solution is uniformly stable (i.e., the solution’s behaviour changes continuously with the data) and consequently it is unique.
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Clark et al. (2026) studied this question.
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