Global Existence and Finite Time Blow-up for the m-Laplacian Parabolic Problem  

作　　者：Yue PANG Vicentiu D.RADULESCU Run Zhang XU 

机构地区：[1]College of Mathematical Sciences,Harbin Engineering University,Harbin 150001,P.R.China [2]Faculty of Applied Mathematics,AGH University of Science and Technology,30-059 Krak´ow,Poland [3]Department of Mathematics,University of Craiova,Street A.I.Cuza No.13,200585 Craiova,Romania

出　　处：《Acta Mathematica Sinica,English Series》2023年第8期1497-1524,共28页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12271122);the China Postdoctoral Science Foundation(Grant No.2013M540270);the Fundamental Research Funds for the Central Universities。

摘　　要：In this paper,we consider an initial boundary value problem of m-Laplacian parabolic equation arising in various physical models.We tackle this problem at three different initial energy levels.For the sub-critical initial energy,we obtain the blow-up result and estimate the lower and upper bounds of the blow-up time.For the critical initial energy,we show the global existence,asymptotic behavior,finite time blow-up and the lower bound of the blow-up time.For the sup-critical initial energy,we prove the finite time blow-up and estimate the lower and upper bounds of the blow-up time.

关 键 词：m-Laplacian parabolic equation BLOW-UP blow-up time global existence 

分 类 号：O175.26[理学—数学]