Complutense University Library

Positivity for large time of solutions of the heat equation: The parabolic antimaximum principle


Díaz Díaz, Jesús Ildefonso and Fleckinger-Pellé, Jacqueline (2004) Positivity for large time of solutions of the heat equation: The parabolic antimaximum principle. Discrete and Continuous Dynamical Systems. Series A., 10 (1-2). pp. 193-200. ISSN 1078-0947

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:


We study the positivity, for large time, of the solutions to the heat equation Q(a) (f,u(0)): [GRAPHIC] where Q is a smooth bounded domain in RN and a C R. We obtain some sufficient conditions for having a finite time t(p) > 0 (depending on a and on the data u(0) and f which are not necessarily of the same sign) such that u(t, x) > 0 For Allt > t(p), a.e.x is an element of Omega.

Item Type:Article
Uncontrolled Keywords:maximum and antimaximum principle; heat equation; parabolic problems
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Differential equations
ID Code:15471

Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, 18, N. 4, 620–709, (1976).

Antontsev, S.N., Diaz, J.I., Shmarev, S.I. Energy Methods for free bounday problems. Applications to nonlinear PDEs and Fluid Mechanics, Series Progress in Nonlinear Differential Equations and Their Applications, No. 48, Birkäuser, Boston, (2002).

Bertsch, M., Peletier, L.A., The asymptotic profile of solutions of a degenerate diffusion equation, Arch. Rat. Mech. Anal. 91, 207–229, (1985).

Ph. Clément, L. A. Peletier, An anti-maximum principle for second order elliptic operators, J. Differential Equations 34, 218–229, (1979).

Díaz, J.I., Morel, J.M., Sur les solutions de l'équation de la chaleur, unpublished manuscript, (1986).

Díaz, J.I., de Thélin, F., On a nonlinear parabolic problem arising in some models related to turbulent flows, SIAM J. Math. Anal., 25, 4, 1085–1111, (1994).

Fleckinger, J., Gossez, J.P., Takáč, P., de Thélin, F., Non existence of solutions and an antimaximum principle for cooperative systems with the p - Laplacian, Math. Nachrichten, 194, 49–78, (1998).

Gmira, A., Véron, L., Asymptotic Behaviour of the Solution of a Semilinear Parabolic Equation, Monatsh.Math. 94, 299–311, (1982).

Sattinger, D., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math J., 21, 979–1000, (1972).

Deposited On:04 Jun 2012 08:40
Last Modified:06 Feb 2014 10:25

Repository Staff Only: item control page