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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On wave fronts propagation in multicomponent media

Author: M. I. Freĭdlin
Journal: Trans. Amer. Math. Soc. 276 (1983), 181-191
MSC: Primary 35B40; Secondary 35K40, 60J60, 92A15
Erratum: Trans. Amer. Math. Soc. 289 (1985), 429.
MathSciNet review: 684501
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Abstract: The behavior as $t \to \infty$ of solutions of some parabolic systems of differential equations of the Kolmogorov-Petrovskii-Piskunov type is investigated. The present approach uses the Kac-Feynman formula and estimates on large deviations.

References [Enhancements On Off] (What's this?)

    A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem, Bjul. Moskov. Gos. Univ. 1, 1-72. M. I. Freidlin, Propagation of a concentration wave in the presence of random motion associated with the growth of a substance, Soviet Math. Dokl. 20 (1979), 503-507. ---, Quasi-linear parabolic equations, and measures on a function space, Funkcional. Anal. i Priložen. 1 (1967), 74-82. ---, Average principle and theorems on large deviations, Russian Math. Surveys 33 (1978). A. D. Wentzell and M. I. Freidlin, Fluctuations in dynamical systems caused by small random pertubations, "Nauka", Moscow, 1979.

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Keywords: Nonlinear diffusion, wave fronts, parabolic systems
Article copyright: © Copyright 1983 American Mathematical Society