论文标题
弗雷德霍姆（Fredholm）转化，用于快速稳定退化抛物线方程
A Fredholm transformation for the rapid stabilization of a degenerate parabolic equation
论文作者
论文摘要
本文介绍了具有正确的Dirich-lelet控制的退化抛物线方程的快速稳定。我们的策略在于采用后退策略，该策略试图找到可逆的转换映射退化的抛物线方程，以稳定成指数稳定的系统，其衰减率是已知的，并且与我们希望的那样大。本文所考虑的转换是弗雷德霍尔姆。它涉及一个至少正式解决另一个PDE的内核。本文的主要目的是证明弗雷德尔姆的转化在自然能量空间中定义明确，连续且可逆。它使我们能够推断出快速稳定。
This paper deals with the rapid stabilization of a degenerate parabolic equation with a right Dirich-let control. Our strategy consists in applying a backstepping strategy, which seeks to find an invertible transformation mapping the degenerate parabolic equation to stabilize into an exponentially stable system whose decay rate is known and as large as we desire. The transformation under consideration in this paper is Fredholm. It involves a kernel solving itself another PDE, at least formally. The main goal of the paper is to prove that the Fredholm transformation is well-defined, continuous and invertible in the natural energy space. It allows us to deduce the rapid stabilization.
