Blow-up phenomena for a class of metaparabolic equations with time dependent coeffcient

AIMS Mathematics

Yadong Shang¹  Huafei Di¹ 

[1] 1 School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510006, P.R. China
2 Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong, 510006, P.R. China;

关键词: metaparabolic equations| blow up| upper bound| lower bound;   

DOI  :  10.3934/Math.2017.4.647

来源: DOAJ

【 摘 要 】

This paper deals with the initial boundary value problem for a metaparabolic equations withtime dependent coeffcient. Under suitable conditions on initial data, a blow-up criterion which ensuresthat u cannot exist all time is given, and an upper bound for blow up time is derived. Moreover, wealso obtain a lower bound for blow-up time if blow up does occur by means of a di erential inequalitytechnique.

【 授权许可】

Unknown