Global well-posedness and exponential stability for heterogeneous anisotropic Maxwell's equations under a nonlinear boundary feedback with delay
Global well-posedness and exponential stability for heterogeneous anisotropic Maxwell's equations under a nonlinear boundary feedback with delay
复制标题
时滞非线性边界反馈下异质各向异性麦克斯韦方程组的全局适定性和指数稳定性
DOI：
10.1016/j.jmaa.2019.02.042
复制
发表时间：
2018
影响因子：
1.3
通讯作者：
Michael Pokojovy
中科院分区：
文献类型：
--
作者：
Andrii Anikushyn;Michael Pokojovy
考虑了有界区域中麦克斯韦方程组的初边值问题，该方程组具有线性非齐次各向异性瞬时材料律，且具有包含瞬时阻尼和局部时滞效应的非线性Silver-Müller型边界反馈机制.通过证明底层非线性生成元的极大单调性，我们在适当的Hilbert空间中建立了整体适定性。在适当的假设和几何条件下，证明了系统是指数稳定的。
We consider an initial–boundary value problem for the Maxwell's system in a bounded domain with a linear nonhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver–Müller-type boundary feedback mechanism incorporating both an instantaneous damping and a time-localized delay effect. By proving the maximal monotonicity property of the underlying nonlinear generator, we establish the global well-posedness in an appropriate Hilbert space. Further, under suitable assumptions and geometric conditions, we show the system is exponentially stable.