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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On wave fronts propagation in multicomponent media
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by M. I. Freĭdlin PDF
Trans. Amer. Math. Soc. 276 (1983), 181-191 Request permission

Erratum: Trans. Amer. Math. Soc. 289 (1985), 429.


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.
    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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 276 (1983), 181-191
  • MSC: Primary 35B40; Secondary 35K40, 60J60, 92A15
  • DOI:
  • MathSciNet review: 684501