Uniform BMO estimate of parabolic equations and global well-posedness of the thermistor problem
数学专题报告
报告题目(Title)：Uniform BMO estimate of parabolic equations and global well-posedness of the thermistor problem
报告人(Speaker)：Prof. Buyang Li (The Hong Kong Polytechnic University)
地点(Place)：后主楼1223
时间(Time)：2025年11月2日（周日）14:30-15:30
邀请人(Inviter)：李海刚
报告摘要
We prove global well-posedness of the time-dependent degenerate thermistor problem by establishing a uniform-in-time bounded mean oscillation (BMO) estimate of inhomogeneous parabolic equations. Applying this estimate to the temperature equation, we derive a BMO bound of the temperature uniform with respect to time, which implies that the electric conductivity is an A_2 weight. The Holder continuity of the electric potential is then proved by applying the De Giorgi–Nash–Moser estimate for degenerate elliptic equations with an A_2 coefficient. The uniqueness of the solution is proved based on the established regularity of the weak solution. Our results also imply the existence of a global classical solution when the initial and boundary data are smooth.
