Geodesic
Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations
Electronic journal of differential equations, Tome 2007 (2007)
In 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.
Classification : 35K55, 35K15, 35A05
Keywords: Bernstein-Nagumo condition, gradient blow-up, a priori estimates nonlinear parabolic equation 
@article{EJDE_2007__2007__a172,
     author = {Tersenov,  Aris S.},
     title = {Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1138.35345},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a172/}
}
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Tersenov,  Aris S. Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a172/