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

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• 作者：K. Oleschko ; A. Yu. Khrennikov
• 关键词：master equation ; geophysics ; water ; in ; oil and oil ; in ; water emulsions ; p ; adic number ; p ; adic diffusion ; quasilinear p ; adic diffusion
• 刊名：Theoretical and Mathematical Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：190
• 期：1
• 页码：154-163
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Applications of Mathematics;
• 出版者：Pleiades Publishing
• ISSN：1573-9333
• 卷排序：190

文摘

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.