Asymptotic gain results for attractors of semilinear systems,Mathematical Control and Related Fields

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Asymptotic gain results for attractors of semilinear systems
Mathematical Control and Related Fields ( IF 1.2 ) Pub Date : 2021-09-08 , DOI: 10.3934/mcrf.2021044
Jochen Schmid ₁ , Oleksiy Kapustyan _{2,

3} , Sergey Dashkovskiy _{2,

3}

Affiliation

<p style='text-indent:20px;'>We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear reaction-diffusion equations comprising disturbed Chaffee–Infante equations, for example.</p>

中文翻译：

半线性系统吸引子的渐近增益结果

<p style='text-indent:20px;'>我们为受干扰的半线性系统建立渐近增益以及输入到状态的实际稳定性结果，以相应的未受干扰系统的全局吸引子为基础。例如，我们将我们的结果应用于包括扰乱 Chaffee-Infante 方程的一大类非线性反应扩散方程。</p>

更新日期：2021-09-08

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