THE GLOBAL SOLUTION AND BLOWUP OF A SPATIOTEMPORAL EIT PROBLEM WITH A DYNAMICAL BOUNDARY CONDITION  

作　　者：谢明洪 谭忠 Minghong XIE;Zhong TAN(School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China;School of Mathematical Science,Xiamen University,Xiamen 361005,China;Shenzhen Research Institute of Xiamen University,Shenzhen 518057,China)

机构地区：[1]School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China [2]School of Mathematical Science,Xiamen University,Xiamen 361005,China [3]Shenzhen Research Institute of Xiamen University,Shenzhen 518057,China

出　　处：《Acta Mathematica Scientia》2023年第4期1881-1914,共34页数学物理学报（B辑英文版）

基　　金：the NNSF of China(12071391);the Guangdong Basic and Applied Basic Research Foundation (2022A1515010069)。

摘　　要：We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent.There are three major ingredients in this paper.The first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial value.The second ingredient is the L^(q)(2 ≤q <∞) estimate of the global solution applying the Moser iteration,which allows us to show that any global solution is a classical solution.The third,which is the main ingredient of this paper,explores the long time asymptotic behavior of global solutions close to the stationary solution and the bubbling phenomenons by means of a concentration compactness principle.

关 键 词：spatiotemporal EIT problem fractional Dirichlet-to-Neumann operator critical exponent bubbling phenomena 

分 类 号：O177[理学—数学]