Research
Non-simultaneous blow-up for a parabolic system with nonlinear boundary flux which obey different laws
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
Citation and License
Boundary Value Problems 2012, 2012:85 doi:10.1186/1687-2770-2012-85
Published: 6 August 2012Abstract
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.
