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Non-simultaneous blow-up for a parabolic system with nonlinear boundary flux which obey different laws

Si Xu1* and Jinfa Zeng2

Author Affiliations

1 Department of Mathematics, Jiangxi Vocational College of Finance and Economics, Jiujiang, Jiangxi, 332000, P.R. China

2 Department of Information Engineering, Jiangxi Vocational College of Finance and Economics, Jiujiang, Jiangxi, 332000, P.R. China

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Boundary Value Problems 2012, 2012:85  doi:10.1186/1687-2770-2012-85

Published: 6 August 2012

Abstract

In this paper, we consider a system of two heat equations with nonlinear boundary flux which obey different laws, one is exponential nonlinearity and another is power nonlinearity. Under certain hypotheses on the initial data, we get the sufficient and necessary conditions, on which there exist initial data such that non-simultaneous blow-up occurs. Moreover, we get some conditions on which simultaneous blow-up must occur. Furthermore, we also get a result on the coexistence of both simultaneous and non-simultaneous blow-ups.

MSC: 35B33, 35K65, 35K55.

Keywords:
simultaneous blow-up; non-simultaneous blow-up; parabolic system; nonlinear boundary flux