Thermoelastic plates with type I heat conduction with second gradient

This article studies the qualitative properties of thermoelastic plates modeled by the second-gradient theory with a Type I heat equation. We establish the exponential stability of the solutions. Our main contribution is to prove that the semigroup is non-differentiable when the bi-Laplacian operator appears in the heat equation. Additionally, we analyze the case where the elastic parameter is negative, demonstrating the uniqueness and instability of the solutions. Finally, in the one-dimensional quasi-static case, we demonstrate the existence and exponential decay of the solutions under specific conditions. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/94/abstr.html