Blow‐up for a class of nonlinear parabolic problems

Article type: Research Article

Authors: Andreu, F. | Mazón, J.M. | Simondon, F. | Toledo, J.

Affiliations: Departamento de Análisis Matemático, Universitat de Valencia, Dr. Moliner 50, 46100 Burjassot, Spain | Université de Besançon et C.N.R.S., Equipe de Matématiques U.A., Faculté des Sciences, F‐25030 Besançon cedex, France

Abstract: For nonlinear parabolic equations of the form ut=Δum−uμ‖∇um‖q+up, we prove nonexistence of global admissible solutions for large initial data for some range of the parameters m, μ, q and p. To do so we use comparison with suitable blowing up self‐similar subsolutions. We also prove that for the complementary range of the parameters for which we obtain blow‐up, there exists globally bounded admissible solutions.

Keywords: nonlinear parabolic equations, admissible solution, finite time blow‐up, gradient term

Journal: Asymptotic Analysis, vol. 29, no. 2, pp. 143-155, 2002