Share This Article:

On the Computation of Extinction Time for Some Nonlinear Parabolic Equations

Abstract Full-Text HTML XML Download Download as PDF (Size:584KB) PP. 754-763
DOI: 10.4236/am.2015.65071    2,285 Downloads   2,677 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Ngarmadji, K. , Ndeuzoumbet, S. , Nkounkou, H. and Mampassi, B. (2015) On the Computation of Extinction Time for Some Nonlinear Parabolic Equations. Applied Mathematics, 6, 754-763. doi: 10.4236/am.2015.65071.

References

[1] Kalashnikov, A.S. (1974) The Propagation of Disturbances in Problems of Non-Linear Heat Conduction with Absorption. USSR Computational Mathematics and Mathematical Physics, 14, 70-85.
http://dx.doi.org/10.1016/0041-5553(74)90073-1
[2] 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
[3] Levine, H.A. (1985) The Phenomenon of Quenching: A Servey. North-Holland Mathematics Studied, 110, 275-286.
http://dx.doi.org/10.1016/S0304-0208(08)72720-8
[4] Diaz, J.I. (2001) Qualitative Study of Nonlinear Parabolic Equations: An Introduction. Extracta Mathematicae, 16, 303-341.
[5] Friedman, A. and Herrero, M.A. (1987) Extinction Properties of Semilinear HEAT Equations with Strong Absorption. Journal of Mathematical Analysis and Applications, 124, 530-546.
http://dx.doi.org/10.1016/0022-247X(87)90013-8
[6] Gu, Y.G. (1994) Necessary and Sufficient Conditions for Extinction of Solutions to Parabolic Equations. Acta Mathematica Sinica, 37, 73-79.
[7] Lair, A.V. (1993) Finite Extinction Time for Solutions of Nonlinear Parabolic Equations. Nonlinear Analysis, Theory, Methods and Applications, 21, 1-8.
[8] Boni, T.K. (2001) Extinction for Dicretizations of Some Semilinear Parabolic Equations. Comptes Rendus de l’Aca- dmie des Sciences de Paris, Serie I, Mathmatique, 333, 795-800.
[9] Mikula, K.B. (1995) Numerical Solution of Nonlinear Diffusion with Finite Extinction Phenomenom. Acta Mathematica Universitatis Comenianae, LXIV, 173-184.
[10] Nabongo, D. and Boni, T.K. (2008) Numerical Quenching for a Semilinear Parabolic Equation. Mathematical Modelling and Analysis, 13, 521-538.
http://dx.doi.org/10.3846/1392-6292.2008.13.521-538
[11] Nabongo, D. and Boni, T.K. (2008) Quenching for Semidiscretization of a Semilinear Heat Equation with Dirichlet and Neumann Boundary Condition. Commentationes Mathematicae Universitatis Carolinae, 49, 463-475.
[12] Lair, A.V. and Oxley, M.K. (1996) Anisotropic Nonlinear Diffusion with Absorption: Existence and Extinction. International Journal of Mathematics and Mathematical Sciences, 19, 427-434.
http://dx.doi.org/10.1155/S0161171296000610
[13] Dumitrache, A. (2007) A Numerical Method to Approximate the Solutions of Nonlinear Absorption Diffusion Equation. Proceeding in Applied Mathematics and Mechanics, 7, 4070041-4070042.
http://dx.doi.org/10.1002/pamm.200701050
[14] Kim, D. and Proskurowski, W. (2004) An Efficient Approach for Solving a Class of Nonlinear 2D Parabolic PDEs. International Journal of Mathematics and Mathematical Sciences, 2004, 881-899.
[15] Griebel, M., Dornseifer, T. and Neunhoeffer, T. (1998) Numerical Simulation in Fluid Dynamics. A Practical Guide, SIAM, Philadephia.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.