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Applications of p-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions

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Abstract

In a very general setting, we discuss possibilities of applying p-adics to geophysics using a p-adic diffusion representation of the master equations for the dynamics of a fluid in capillaries in porous media and formulate several mathematical problems motivated by such applications. We stress that p-adic wavelets are a powerful tool for obtaining analytic solutions of diffusion equations. Because p-adic diffusion is a special case of fractional diffusion, which is closely related to the fractal structure of the configuration space, p-adic geophysics can be regarded as a new approach to fractal modeling of geophysical processes.

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Authors and Affiliations

  1. Centro de Geociencias, Universidad Nacional Autónoma de México (UNAM), Campus UNAM Juriquilla, Querétaro, México

    K. Oleschko

  2. International Center for Mathematical Modelling in Physics and Cognitive Sciences, Mathematical Institute, Linnaeus University, Växjö, Sweden

    A. Yu. Khrennikov

Authors
  1. K. Oleschko
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  2. A. Yu. Khrennikov
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Correspondence to A. Yu. Khrennikov.

Additional information

This paper was financially supported by the project SENER-CONACYT-Hidrocarburos, Yacimiento Petrolero como un Reactor Fractal, N 168638 and the Consejo Nacional de Ciencia y Tecnolog´ıa (CONACYT), Mexico, under grant 312-2015, Fronteras de la Ciencia.

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 1, pp. 179–190, January, 2017.

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Oleschko, K., Khrennikov, A.Y. Applications of p-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions. Theor Math Phys 190, 154–163 (2017). https://doi.org/10.1134/S0040577917010135

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