Backward Uniqueness for the Heat Equation in Cones
主 题: Backward Uniqueness for the Heat Equation in Cones
报告人: Dr. Jie Wu (BICMR)
时 间: 2015-03-24 14:00 - 15:00
地 点: Room 77201 at #78 courtyard, BICMR
The Backward Uniqueness(BU) property is applied in many problems, such as the control theory for PDEs and the regularity theory of parabolic equations. Especially, it plays an important role in the proof of critical regularity for Navier–Stokes equations. In the past, the BU for the heat equation in total space, the exterior domain and half space have already been established, but the problem in cones is still open and rather interesting. First, Escauriaza constructed an example to show that BU fails when the opening angle of the cone is less than 90 degree, and 90 degree is the borderline case for Escauriaza's construction. Later, Lu Li and ?verák proved that BU holds when the angle is larger than 109.5 degree. Inspired by the above results, it is conjectured naturally that BU holds when the angle is larger than 90 degree and fails when it is less than 90 degree. Here we improve the result of Lu Li and ?verák and show that BU holds when the angle is larger than 99 degree by exploring a new type of Carleman inequality.