Aris S. Tersenov
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.
Show me the PDF file (285K), TEX file, and other files for this article.
| Aris S. Tersenov Department of Mathematics and Statistics University of Cyprus P.O. Box 20537, 1678 Nicosia, Cyprus Tel.:+357 22892560, Fax:+357 22892550 email: aterseno@ucy.ac.cy |
Return to the EJDE web page