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Zbl 1203.35150
Mu, Chunlai; Liu, Dengming; Zhou, Shouming
Properties of positive solutions for a nonlocal reaction-diffusion equation with nonlocal nonlinear boundary condition. (English)
[J] J. Korean Math. Soc. 47, No. 6, 1317-1328 (2010). ISSN 0304-9914

Summary: We study properties of positive solutions for the reaction-diffusion equation $u_t = \Delta u + \int _{\Omega }u^p dx - ku^q$ in $\Omega \times (0,T)$ with nonlocal nonlinear boundary condition $u(x,t) = \int _{\Omega }f(x,y)u^l (y,t) \,dy$ on $\partial \Omega \times (0,T)$ and nonnegative initial data $u_0(x)$, where $p, q, k, l>0$. Some conditions for the existence and nonexistence of global positive solutions are given.

MSC 2000:: *35K61
35B35 Stability of solutions of PDE
35K57 Reaction-diffusion equations
35K65 Parabolic equations of degenerate type
35R09
35B44
35B09

Keywords: global existence; blow-up

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