| Summary: | We consider a class of nonlinear parabolic equation with general source function f(u), conduction function g(u) and conduction coefficient ρ(|∇u|2) in multi-dimensional space. We establish new control conditions to guarantee that the positive solution exists globally. At the same time, under suitable control conditions, by means of the Sobolev inequality in multi-dimensional space, we obtain upper and lower bounds of the blow-up time t∗ in Rn (n ⩾ 2). Our work generalize the models, improve the method and remove the constraint of spatial dimension in many literatures. © 2022, Wilmington Scientific Publisher. All rights reserved.
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