-д хадгалсан:
Номзүйн дэлгэрэнгүй
Үндсэн зохиолч: Vanlaere, Roman
Формат: Preprint
Хэвлэсэн: 2026
Нөхцлүүд:
Онлайн хандалт:https://arxiv.org/abs/2602.08044
Шошгууд: Шошго нэмэх
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
Агуулга:
  • We study the observability properties of the Grushin equation with an inverse square potential, whose singularity occurs at the boundary of two-dimensional rectangular domains or in the interior of the domain in higher dimensions. In some specific configurations of the observation set, we obtain the exact minimal time of observability. The analysis we present relies on recent Carleman estimates obtained by K. Beauchard, J. Dardé, and S. Ervedoza. As a byproduct of these results, we observe, for the heat equation associated to the Laplace-Beltrami operator on almost-Riemannian manifolds, a dependence of the minimal time of observability on the dimension of the singularity.