论文标题
通过关闭与耗散和港口哈米尔顿港系统应用的关闭关系的稳定性
Stability via closure relations with applications to dissipative and port-Hamiltonian systems
论文作者
论文摘要
我们认为可以通过更简单的操作员$ a _ {\ propatatorName {ext}} $来代表的差分运算符$ a $，可以通过所谓的闭合关系表示。我们分析了$ a $和$ a _ {\ operatorname {ext}} $的光谱属性如何相关，并给出足够的条件，以提供由$ a $ a $ a $ a $ a $ a _ _ _ {\ operatorname {ext}} $产生的半群生成的半群的指数稳定性。 作为应用，我们研究了耦合波热系统在间隔上的长期行为，由矩阵有价值电位耦合的有界域的抛物线方程，以及线性无限二维港口 - 哈米尔顿港系统，并在间隔上进行耗散。
We consider differential operators $A$ that can be represented by means of a so-called closure relation in terms of a simpler operator $A_{\operatorname{ext}}$ defined on a larger space. We analyze how the spectral properties of $A$ and $A_{\operatorname{ext}}$ are related and give sufficient conditions for exponential stability of the semigroup generated by $A$ in terms of the semigroup generated by $A_{\operatorname{ext}}$. As applications we study the long-term behaviour of a coupled wave-heat system on an interval, parabolic equations on bounded domains that are coupled by matrix valued potentials, and of linear infinite-dimensional port-Hamiltonian systems with dissipation on an interval.
