Pseudo-differential equations with weak degeneration for radial functions of p-adic argument

In paper A. N. Kochubei ((2014) [3]) a right inverse to Vladimirov-Taibleson fractional differential operator Dα,α>0 was found. It turns out that this permits to reduce the p-adic Cauchy problem for radial functions to an integral equation whose properties resemble those of classical Volterra equ...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2023-07, Vol.523 (2), p.127026, Article 127026
Main Authors: Antoniouk, Alexandra V., Kochubei, Anatoly N., Serdiuk, Mariia V.
Format: Article
Language:English
Subjects:
Cauchy problem
Fractional differential operator
p-adic analysis
Radial functions
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Summary:In paper A. N. Kochubei ((2014) [3]) a right inverse to Vladimirov-Taibleson fractional differential operator Dα,α>0 was found. It turns out that this permits to reduce the p-adic Cauchy problem for radial functions to an integral equation whose properties resemble those of classical Volterra equations. In this article, we develop further these ideas to an important class of degenerate pseudo-differential equations with operator Dα,α>0. We find the conditions of local and global solvability for corresponding nonlinear weakly degenerate equations.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127026