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EXISTENCE AND BLOW-UP OF SOLUTIONS TO A PARABOLIC EQUATION WITH NONSTANDARD GROWTH CONDITIONS

Part of: Parabolic equations and systems Partial differential equations

Published online by Cambridge University Press:  11 December 2018

YANG LIU Open the ORCID record for YANG LIU [Opens in a new window]
YANG LIU*
Affiliation:
College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730124, PR China College of Mathematics, Sichuan University, Chengdu 610065, PR China email liuyangnufn@163.com
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Abstract

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We study the initial boundary value problem for a fourth-order parabolic equation with nonstandard growth conditions. We establish the local existence of weak solutions and derive the finite time blow-up of solutions with nonpositive initial energy.

Keywords

fourth-order parabolic equationexistenceblow-up

MSC classification

Primary: 35K35: Initial-boundary value problems for higher-order parabolic equations
Secondary: 35A01: Existence problems 35B44: Blow-up
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 242 - 249
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was supported by the Science and Technology Plan Project of Gansu Province in China (Grant No. 17JR5RA279) and the Talent Introduction Research Project of Northwest Minzu University in China (Grant No. xbmzdxyjrc201701).

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