The Dissipative Bresse-Timoshenko System without a Second Spectrum is Well-Posedness and Exponential Stability

Aims: This paper investigates the dissipative Bresse-Timoshenko system without second spectrum. Study Design: Cross-sectional study.Place and Duration of Study: This paper was completed at the School of Mathematics and Statistics at Southwest University during from May 2023 to February 2024.Methodology: Using the theory of C0-semigroup.Results: The results show that the suitability of the system solution is established and the exponential stability is established.Conclusion: The C0-semigroup theory are applied to study the well-posedness and exponential stability, which is different from others, where the multiplying method and energy method were used to study the exponential stability. This result substantially improves earlier results in the literature.