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 Blow-up and global solutions for some parabolic systems under nonlinear boundary conditions J. Korean Math. Soc.Published online 2019 Apr 10 Limin Guo, Lishan Liu, Yonghong Wu, and Yumin Zou Qufu Normal University, Curtin University, Shandong University of Science and Technology Abstract : In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $(\varrho(u))_{t}$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs. Keywords : Blows-up and global solutions; Parabolic equations; Nonlinear boundary conditions; Time dependent coefficients; Abstract form of $(\varrho(u))_{t}$ MSC numbers : 35K55, 35K60 Full-Text :