Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations
Date
2007-04-17
Authors
Tersenov, Aris
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Bernstein-Nagumo condition, Gradient blow-up, A priori estimates nonlinear parabolic equation
Citation
Tersenov, 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.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.