摘要
本文研究一类带奇异项的退化Grushin方程的零控问题.不同于Fourier分解的方法,通过选择一类特殊的势函数,我们证明了退化Grushin算子的Carleman估计.然后利用此Carleman估计,给出带奇异项的退化Grushin方程的观测不等式,获得该方程的零控结果.
This paper concerns null controllability for a parabolic operator of Grushin type with degeneracy of the diffusion coefficient and singularity of the potential occurring on boundary. Different from the existing Fourier decomposition method to deal with degenerate Grushin operator, we choose a special weight function to prove a new Carleman estimate for the whole Grushin operator with singular potential, not only for its Fourier components. An observability inequality is obtained by means of this Carleman estimate.Then under a suitable geometrical condition on the control domain, we show that the null controllability holds in any time for any degeneracy γ 0.
出处
《应用数学》
CSCD
北大核心
2018年第1期188-201,共14页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China(11601240)
