In this paper, exponential stabilisation and dissipativity analysis for the scalar distributed parameter system governed by semilinear partial differential equations (PDE) are investigated. The PDE under consideration is the parabolic type with unstable dynamics and assumed to have an external disturbance and mixed boundary conditions. First, the existence and uniqueness results for the PDE are discussed using semigroup theory. Then the sufficient conditions to guarantee the exponential stability and dissipativity are obtained using the Lyapunov stability theory. Finally, the results are verified through numerical examples.

中文翻译：

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半线性抛物线系统的指数稳定和耗散分析

本文研究了半线性偏微分方程(PDE)控制的标量分布参数系统的指数镇定和耗散分析。所考虑的偏微分方程是具有不稳定动力学的抛物线类型，并假定具有外部干扰和混合边界条件。首先，使用半群理论讨论了偏微分方程的存在性和唯一性结果。然后利用李雅普诺夫稳定性理论得到保证指数稳定性和耗散性的充分条件。最后通过数值算例验证了结果。