论文标题
半线性演化方程的流量和特性
Well-posedness and properties of the flow for semilinear evolution equations
论文作者
论文摘要
我们得出了具有无界输入操作员的半线性演化方程的良好状态的条件。基于此，我们为流程图的此类属性提供了足够的条件，例如Lipschitz的连续性，界限 - 接触性能，可及性集的界限等。这些属性代表了半线性边界控制系统的稳定性和稳健性分析的基本工具箱。 我们涵盖了一般$ C_0 $ -Semigroups和可能具有边界和分布式干扰的分析半群。我们以非线性局部动力学以及分布和边界干扰的汉堡方程式进行了说明。
We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity, bounded-implies-continuation property, boundedness of reachability sets, etc. These properties represent a basic toolbox for stability and robustness analysis of semilinear boundary control systems. We cover systems governed by general $C_0$-semigroups, and analytic semigroups that may have both boundary and distributed disturbances. We illustrate our findings on an example of a Burgers' equation with nonlinear local dynamics and both distributed and boundary disturbances.
