Abstract
In this paper, we analyze the nonlinear thermoelastic plates, with Fourier heat conduction, and consider a polynomial-type nonlinearity. We first develop a theoretical analysis of the corresponding linear system to derive time decay estimates in and . Then, using that set of decay estimates and controlling the nonlinearity, we prove the existence and uniqueness of local solutions with initial data , with , and , for .
Acknowledgements
The first author has been supported by Universidad de Córdoba, Project FCB-05-22. The third author has been supported by Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander and Project CIPIF-MATH-AmSud de 2022. The authors would like to thank the anonymous referees for useful remarks and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).