Journal of East China Normal University(Natural Science) ›› 2022, Vol. 2022 ›› Issue (6): 30-37.doi: 10.3969/j.issn.1000-5641.2022.06.004

• Mathematics • Previous Articles     Next Articles

Blow-up phenomenon of a parabolic system with a nonlinear gradient term

Yuanfei LI()   

  1. School of Data Science, Guangzhou Huashang College, Guangzhou 511300, China
  • Received:2021-02-01 Online:2022-11-25 Published:2022-11-22

Abstract:

In this paper, the blow-up problem of a parabolic equation with a nonlinear gradient term in finite time is studied. By constructing an auxiliary function, using the method of energy estimation and the differential inequality technique, the lower bound of blow-up time is obtained. After limiting the parameters of the equation, the existence of a global solution is proved.

Key words: nonlinear gradient term, blow-up, lower bound, global existence

CLC Number: