Blow-up and global solutions for some parabolic systems under nonlinear boundary conditions
J. Korean Math. Soc. 2019 Vol. 56, No. 4, 1017-1029
https://doi.org/10.4134/JKMS.j180539
Published online July 1, 2019
Limin Guo, Lishan Liu, Yonghong Wu, Yumei Zou
Changzhou Institute of Technology; Curtin 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, 35K61
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