论文标题
退化/奇异抛物线方程的边界控制的存在和成本
Existence and cost of boundary controls for a degenerate/singular parabolic equation
论文作者
论文摘要
在本文中，我们考虑以下退化/单数抛物线方程$$ u_t-（x^αu_{x}）_ x - x - \fracμ{x^{2-α}} u = 0，\ qquad x \ qquad x \ in（0,1），\ t in（0,1） （1-α）^2/4 $是两个实际参数。 我们通过$ h^1（0，t）$控制作用于$ x = 1 $或变性和奇异性$ x = 0 $。此外，我们对两种情况下的可控成本进行了详尽的估计。这些证明是基于Fattorini和Russell的经典力矩方法，以及对生物三相序列的最新结果。
In this paper, we consider the following degenerate/singular parabolic equation $$ u_t -(x^αu_{x})_x - \fracμ{x^{2-α}} u =0, \qquad x\in (0,1), \ t \in (0,T), $$ where $0\leq α<1$ and $μ\leq (1-α)^2/4$ are two real parameters. We prove the boundary null controllability by means of a $H^1(0,T)$ control acting either at $x=1$ or at the point of degeneracy and singularity $x=0$. Besides we give sharp estimates of the cost of controllability in both cases in terms of the parameters $α$ and $μ$. The proofs are based on the classical moment method by Fattorini and Russell and on recent results on biorthogonal sequences.
