<Emphasis Type="Italic">p</Emphasis>-Adic Analogue of the Porous Medium Equation |
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Authors: | Andrei?Yu?Khrennikov Email author" target="_blank">Anatoly?N?KochubeiEmail author |
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Institution: | 1.International Center for Mathematical Modeling in Physics and Cognitive Sciences, Mathematical Institute,Linnaeus University,V?xj?,Sweden;2.Institute of Mathematics,National Academy of Sciences of Ukraine,Kiev,Ukraine |
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Abstract: | We consider a nonlinear evolution equation for complex-valued functions of a real positive time variable and a p-adic spatial variable. This equation is a non-Archimedean counterpart of the fractional porous medium equation. Developing, as a tool, an \(L^1\)-theory of Vladimirov’s p-adic fractional differentiation operator, we prove m-accretivity of the appropriate nonlinear operator, thus obtaining the existence and uniqueness of a mild solution. We give also an example of an explicit solution of the p-adic porous medium equation. |
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