Abstract
In this paper we’ll describe physical effects of localization and intermittency for the particle system with branching and diffusion in the random environment. Such type of models can arise in chemical kinetics in the case (for instance) of randomly distributed grains of a catalyst. In terms of PDE’s it is a problem of the asymptotic structure of the solutions for the non-linear reaction-diffusion equations with a random reaction rate.
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References
Kolmogorov, A, Petrovski, I., Piskunov, N., Etude de l’equation de la diffusion avec croissance de la quantite de la matiere et son application a un probleme biologique, Moscow Univers. Math. Bull., I, 1–25 (1937).
Harris, T., Branching processes, Springer-Verlag, New York, 1979.
Sevastjanov, B.A., Branching processes, Moscow, Nauka, 1971.
Gichman, I., Skorkhod, A., Introduction to the Theory of Random Processes, Moscow, Nauka, 1965.
Aizenman, M., Molchanov, S., Localization at large disorder and large energies: an elementary derivation, Comm. Math. Phys., 157, 245–278 (1993).
Carmona, R., Lacroix, J., Spectral theory of Random Schrödinger operator, Boston, Birkhaiiser, 1990.
Pastur, L., Figotin, A., Spectra of Random and Almost-Periodic Operators, Berlin, Springer-Verlag, 1992.
Zeldovich, Ja., Molchanov, S., Ruzmaikin, A., Sokolov, D., Intermittency diffusion and generation in a nonstationary random medium, Soy. Sci. Rev., 7 Sec C, Y, 1–110 (1988).
Gärtner, J., Molchanov, S., Parabolic problem for the Anderson model, Comm Math. Phys., 132, 613–655 (1990).
Carmona, R., Molchanov, S., Parabolic Anderson model and intermittency, Mem. Amer. Math. Soc., 106, 125 (1994).
Molchanov, S., Ruzmaikin, A., Cell-dynamo in non-stationary media, Proc. of E. Dynkin Conference, 1994, Cornell Univ., Boston, Birkhaiiser.
Molchanov, S., Ideas in the theory of random media, Acta Appl. Math. 22, 223 (1991).
Molchanov, S., Lectures on random media, Saint-Flour Summer School on Probability, Lecture Notes in Math., 1581, Springer-Verlag, 242–411,1994.
Feller, W., Introduction to the Probability Theory and Applications, v.1I, New York, J. Wiley and Sons, 1984.
Gärtner, J., On propagation of the wave fronts in the random media, Math. Nachr. 100, 271–296 (1981).
Freidlin, M, Limit theorems for large deviations and reaction-diffusion equations, Ann. of Probab., 13, # 3, 639–675 (1986).
Jarovaja, L., Ph.D. thesis, Moscow State Univ., 1991.
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Molchanov, S. (1996). Reaction-Diffusion Equations in the Random Media: Localization and Intermittency. In: Funaki, T., Woyczynski, W.A. (eds) Nonlinear Stochastic PDEs. The IMA Volumes in Mathematics and its Applications, vol 77. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8468-7_5
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DOI: https://doi.org/10.1007/978-1-4613-8468-7_5
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