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p-Adic Analogue of the Porous Medium Equation
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
National Academy of Sciences of Ukraine, Ukraine.
2017 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, p. 1-24Article in journal (Refereed) Epub ahead of print
Abstract [en]

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 nonArchimedean counterpart of the fractional porous medium equation. Developing, as a tool, an L1-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.

Place, publisher, year, edition, pages
USA, 2017. p. 1-24
Keyword [en]
Mild solution of the Cauchy problem; p-adic numbers; p-adic porous medium equation; Vladimirov’s p-adic fractional differentiation operator
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-72074DOI: 10.1007/s00041-017-9556-4OAI: oai:DiVA.org:lnu-72074DiVA, id: diva2:1194640
Available from: 2018-04-03 Created: 2018-04-03 Last updated: 2018-05-16

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Khrennikov, Andrei

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