Tersenov, Aris2021-08-062021-08-062007-04-17Tersenov, A. S. (2007). Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations. Electronic Journal of Differential Equations, 2007(57), pp. 1-12.1072-6691https://hdl.handle.net/10877/14218In this paper we study the initial-boundary value problems for nonlinear parabolic equations without Bernstein-Nagumo condition. Sufficient conditions guaranteeing the nonexistence of gradient blow-up are formulated. In particular, we show that for a wide class of nonlinearities the Lipschitz continuity in the space variable together with the strict monotonicity with respect to the solution guarantee that gradient blow-up cannot occur at the boundary or in the interior of the domain.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalBernstein-Nagumo conditionGradient blow-upA priori estimates nonlinear parabolic equationArticle