AIMS Mathematics, 2017, 2(4): 647-657. doi: 10.3934/Math.2017.4.647

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

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

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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.
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