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Global blow-up for a localized nonlinear parabolic equation with a nonlocal boundary condition. (English) Zbl 1227.35090
Summary: This paper deals with the blow-up properties of positive solutions to a nonlinear parabolic equation of the type $$u_t=f(u)\big(\Delta u+au(x_0,t)\big), \quad x\in\Omega,$$ with a localized reaction source and a nonlocal boundary condition. Under certain conditions, blow-up criteria are established. Furthermore, when $f(u)=u^p$, $0<p\le 1$, the global blow-up behavior is shown, and the blow-up rate estimates are also obtained.

##### MSC:
 35B44 Blow-up (PDE) 35K59 Quasilinear parabolic equations 35K20 Second order parabolic equations, initial boundary value problems
##### Keywords:
localized reaction source; blow-up rate
Full Text:
##### References:
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