### Impacto

Friedman, Avner and Herrero, Miguel A.
(1992)
*Extinction and positivity for a system of semilinear parabolic variational inequalities.*
Journal of Mathematical Analysis and Applications, 167
(1).
pp. 167-175.
ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/0022247X92902448

## Abstract

A simple model of chemical kinetics with two concentrations u and v can be formulated as a system of two parabolic variational inequalities with reaction rates v(p) and u(q) for te diffusion processes of u and v, respectively. It is shown that if pq < 1 and the initial values of u and v are “comparable” then at least one of the concentrations becomes extinct in finite time. On the other hand, for any p = q > 0 there are initial values for which both concentrations do not become extinct in any finite time.

Item Type: | Article |
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Uncontrolled Keywords: | Model of chemical kinetics with two concentrations |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 17417 |

References: | S. N. ANTONCEV, On the localization of solutions of nonlinear degenerate elliptic and parabolic equations, Soviet Math. Dokl. 24 (1981), 420-424. H. BREZIS AND A. FRIEDMAN, Estimates on the support of solutions of parabolic variational inequalities, Illinois J. Math. 20 (1976), 82-97. L. C. EVANS AND B. F. KNERR, Instantaneous shrinking of the support of nonnegative solutions to certain parabolic equations and variational inequalities, Illinois J. Much. 23(1979), 153-166. A. FRIEDMAN, “Variational Principles and Free Boundary Problems,” Wiley, New York, 1982. A. FRIEDMAN AND M. A. HERRERO, Extinction properties of semilinear heat equations with strong absorption, J. Math. Anal. Appl. 124 (1987), 550-546. M. A. HERRERO AND J. J. L. VELÁZQUEZ, Approaching an extinction point in semilinear heat equations with strong absorption, to appear. A. S. KALASHNIKOV, The propagation of disturbances in problems of nonlinear heat conduction with absorption, U.S.S.R. Comput. Math. and Math. Phys. 14 (1974), 70-85. |

Deposited On: | 13 Dec 2012 09:41 |

Last Modified: | 07 Feb 2014 09:47 |

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