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Galaktionov, V.A. and Vasquez, J.L. (2002) The Problem of Blow-Up in Nonlinear Parabolic Equations. Discrete and Continuous Dynamics Systems, 8, 399-433.
http://dx.doi.org/10.3934/dcds.2002.8.399

has been cited by the following article:

• TITLE: On the Computation of Extinction Time for Some Nonlinear Parabolic Equations

  AUTHORS: Kossadoum Ngarmadji, Siniki Ndeuzoumbet, Hilaire Nkounkou, Benjamin Mampassi

  KEYWORDS: Nonlinear Parabolic Equations, Donor-Cell Scheme, Numerical Extinction Time, General Domains

  JOURNAL NAME: Applied Mathematics, Vol.6 No.5, May 7, 2015

  ABSTRACT: The phenomenon of extinction is an important property of solutions for many evolutionary equa-tions. In this paper, a numerical simulation for computing the extinction time of nonnegative solu-tions for some nonlinear parabolic equations on general domains is presented. The solution algo-rithm utilizes the Donor-cell scheme in space and Euler’s method in time. Finally, we will give some numerical experiments to illustrate our algorithm.