论文标题
具有非线性动态边界条件的波方程的速度稳定
Velocity Stabilization of a Wave Equation with a Nonlinear Dynamic Boundary Condition
论文作者
论文摘要
本文处理具有非线性动态边界条件的一维波方程，而诺伊曼型边界控制作用在另一个末端。我们考虑一类非线性稳定反馈，仅取决于受控肢体的速度。不受控制的边界受到非线性一阶项的约束，这可能代表非线性边界反阻尼。初始数据是在与问题相关的最佳能源空间中获取的。在不同情况下研究了机械能的指数衰减。建立了合适的不变集的稳定性和吸引力。
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on the velocity at the controlled extremity. The uncontrolled boundary is subject to a nonlinear first-order term, which may represent nonlinear boundary anti-damping. Initial data is taken in the optimal energy space associated with the problem. Exponential decay of the mechanical energy is investigated in different cases. Stability and attractivity of suitable invariant sets are established.
