In this paper we study the boundary stabilization of a one-dimensional thermoelastic diffusion problem of type II. The system of equations is a coupling of three hyperbolic equations. This poses some new mathematical and numerical difficulties. With the help of the semigroup theory of linear operators, we prove the well-posedness of the proposed problem. By using the frequency domain method combined with the multiplier technique, we prove the exponential stability of the solutions. Finally, we present a numerical scheme based on the Chebyshev spectral method and we give two numerical examples to validate the proposed model and to show its capability.

中文翻译：

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II型热弹性扩散系统的边界稳定

在本文中，我们研究了II型一维热弹性扩散问题的边界稳定。方程组是三个双曲方程的耦合。这带来了一些新的数学和数值困难。借助线性算子的半群理论，我们证明了所提出问题的适定性。通过将频域方法与乘数技术相结合，我们证明了解的指数稳定性。最后，我们提出了一种基于Chebyshev谱方法的数值方案，并给出了两个数值例子来验证所提出的模型并展示其功能。