Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 57, pp. 1-12.

Title: Sufficient conditions for nonexistence of gradient
       blow-up for  nonlinear parabolic equations

Author: Aris S. Tersenov (Univ. of Cyprus, Cyprus)

Abstract:
 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.
  
Submitted February 8, 2006. Published April 17, 2007.
Math Subject Classifications: 35K55, 35K15, 35A05.
Key Words: Bernstein-Nagumo condition; gradient blow-up;
           a priori estimates nonlinear parabolic equation.