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Blow-up for degenerate parabolic equations with nonlocal source

Authors:	Youpeng Chen Qilin Liu Chunhong Xie

Institution:	Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China ; Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China Chunhong Xie ; Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China

Abstract:	This paper deals with the blow-up properties of the solution to the degenerate nonlinear reaction diffusion equation with nonlocal source $x^{q}u_{t}-(x^{\gamma}u_{x})_{x}=\int_{0}^{a}u^{p}dx$ in $(0,a)\times (0,T)$ subject to the homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally or blows up in finite time are obtained. Furthermore, it is proved that under certain conditions the blow-up set of the solution is the whole domain.

Keywords:	Degenerate nonlocal problem classical solution global existence blow-up set

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