Geodesic
Applications of $p$-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 179-190

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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.
Keywords: master equation, geophysics, water-in-oil and oil-in-water emulsions, $p$-adic number
Mots-clés : $p$-adic diffusion, quasilinear $p$-adic diffusion. 
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     author = {K. Oleschko and A. Yu. Khrennikov},
     title = {Applications of $p$-adics to geophysics: {Linear} and quasilinear diffusion of water-in-oil and oil-in-water emulsions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {1},
     year = {2017},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a12/}
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K. Oleschko; A. Yu. Khrennikov. Applications of $p$-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 179-190. http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a12/