Blow-up phenomena for a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions

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Abstract

This paper is concerned with the blow-up of the solution to a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions. Lower bound for blow-up time is derived when the blow-up does occur.

Keywords

Blow-up
Nonlinear boundary conditions
Lower bound
Parabolic problems

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The work was supported by the national natural Science Foundation of China (Grants 11201087, 11001088), Science Foundation of Guangdong University of Finance (Grant 11XJ01-04), the Natural Science Foundation of Guangdong Province, China (Grant S2011040000805), and Foundation for Distinguished Young Talents in Higher Education of Guangdong, China (Grant 2012LYM_0098).