
handle: 11311/1216758
<p style='text-indent:20px;'>We provide a complete stability analysis for the abstract differential system made by an antidamped wave-type equation, coupled with a dissipative heat-type equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{cases} u_{tt} + A u -\gamma u_t = p A^{\alpha} \theta \\ \theta_{t} + \kappa A^{\beta} \theta = - p A^{\alpha} u_t \end{cases} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ A $\end{document}</tex-math></inline-formula> is a strictly positive selfadjoint operator on a Hilbert space, <inline-formula><tex-math id="M2">\begin{document}$ \gamma, \kappa>0 $\end{document}</tex-math></inline-formula>, and both the parameters <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \beta $\end{document}</tex-math></inline-formula> can vary between <inline-formula><tex-math id="M5">\begin{document}$ 0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ 1 $\end{document}</tex-math></inline-formula>. The asymptotic properties of the associated solution semigroup are determined by the strength of the coupling, as well as the quantitative balance between the antidamping <inline-formula><tex-math id="M7">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula> and the damping <inline-formula><tex-math id="M8">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula>. Depending on the value of <inline-formula><tex-math id="M9">\begin{document}$ (\alpha, \beta) $\end{document}</tex-math></inline-formula> in the unit square, one of the following mutually disjoint situations can occur: either the related semigroup decays exponentially fast, or all the solutions vanish but not uniformly, or there exists a trajectory whose norm blows up exponentially fast as <inline-formula><tex-math id="M10">\begin{document}$ t\to\infty $\end{document}</tex-math></inline-formula>.</p><p style='text-indent:20px;'> </p><p style='text-indent:20px;'>Correction: Sections 7, 8 and 9 are missing from this article. Such sections were present and peer-reviewed in the original submission, but they were mistakenly omitted during the preparation of the final version with the AIMS template. They are added in <a href="https://www.aimsciences.org/article/doi/10.3934/dcdss.2022125" target="_blank">Correction to “Thermoelasticity with antidissipation” (volume 15, number 8, 2022, 2173-2188)</a>.</p>
damping and anti-damping, exponential blow up, PDEs in connection with classical thermodynamics and heat transfer, exponential stability, Asymptotic behavior of solutions to PDEs, damping and antidamping, stability, Fourier heat conduction law, Thermal effects in solid mechanics, thermoelasticity, Classical linear elasticity, Thermoelasticity
damping and anti-damping, exponential blow up, PDEs in connection with classical thermodynamics and heat transfer, exponential stability, Asymptotic behavior of solutions to PDEs, damping and antidamping, stability, Fourier heat conduction law, Thermal effects in solid mechanics, thermoelasticity, Classical linear elasticity, Thermoelasticity
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