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

Guo, Limin;Liu, Lishan;Wu, Yonghong;Zou, Yumei

• Received : 2018.08.07
• Accepted : 2019.03.04
• Published : 2019.07.01
• 18 0

#### 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 $({\varrho}(u))_t$

#### Acknowledgement

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