# BLOW-UP AND GLOBAL SOLUTIONS FOR SOME PARABOLIC SYSTEMS UNDER NONLINEAR BOUNDARY CONDITIONS

• Guo, Limin (School of Mathematical Sciences Qufu Normal University) ;
• Liu, Lishan (School of Mathematical Sciences Qufu Normal University) ;
• Wu, Yonghong (Department of Mathematics and Statistics Curtin University) ;
• Zou, Yumei (Department of Statistics and Finance Shandong University of Science and Technology)
• Accepted : 2019.03.04
• Published : 2019.07.01
• 131 17

#### 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.

#### Acknowledgement

Supported by : National Natural Science Foundation of China, Natural Science Foundation of Shandong Province of China, Changzhou institute of technology

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