This is the first paper of a trilogy intended by the authors in what concerns a unified approach to the stability of thermoelastic arched beams of Bresse type under Fourier’s law. Our main goal in this starting work is to develop an original observability inequality for conservative Bresse systems with non-constant coefficients. Then, as a powerful application, we prove mathematically that the stability of a partially damped model in thermoelastic Bresse beams is invariant under the boundary conditions. The exponential and optimal polynomial decay rates are addressed. This approach gives a new view on the stability of Bresse systems subject to different boundary conditions as well as it provides an accurate answer for the related issue raised by Liu and Rao (Z. Angew. Math. Phys. 60(1): 54–69, 2009) from both the physical and mathematical points of view.

这是作者打算发表的三部曲的第一篇论文，涉及在傅立叶定律下采用统一方法来稳定Bresse型热弹性拱形梁的稳定性的方法。我们在这项开始工作中的主要目标是为具有非恒定系数的保守Bresse系统开发原始的可观测性不等式。然后，作为有力的应用，我们用数学方法证明了在边界条件下热弹性Bresse梁中部分阻尼模型的稳定性是不变的。提出了指数和最优多项式衰减率。这种方法为Bresse系统在不同边界条件下的稳定性提供了新的观点，并且为Liu和Rao提出的相关问题提供了准确的答案（Z. Angew。Math。Phys。60（1）：54– 69，