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http://dx.doi.org/10.4134/JKMS.j180539

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)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.4, 2019 , pp. 1017-1029 More about this Journal
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 $({\varrho}(u))_t$;
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