Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations
Texas State University-San Marcos, Department of Mathematics
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.
Bernstein-Nagumo condition, Gradient blow-up, A priori estimates nonlinear parabolic equation
Tersenov, A. S. (2007). Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations. <i>Electronic Journal of Differential Equations, 2007</i>(57), pp. 1-12.
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