\(p\) -adic semilinear evolutionary pseudodifferential equations in Lizorkin spaces

DOI10.1134/S1064562407040151zbMath1162.35076OpenAlexW2143186334MaRDI QIDQ2377517

Sergio A. Albeverio, Andrei Yu. Khrennikov, Vladimir Shelkovich

Publication date: 19 January 2009

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562407040151

zbMATH Keywords

pseudodifferential equations\(p\)-adic analysis

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10) Pseudodifferential operators (47G30) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (11)

\(p\)-adic mathematical physics: the first 30 years ⋮ The Cauchy problems for evolutionary pseudo-differential equations over \(p\)-adic field and the wavelet theory ⋮ Semi-linear Cauchy problem and Markov process associated with a \(p\)-adic non-local ultradiffusion operator ⋮ Solving nonlinear \(p\)-adic pseudo-differential equations: combining the wavelet basis with the Schauder fixed point theorem ⋮ Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity ⋮ Blow-up phenomena for \(p\)-adic semilinear heat equations ⋮ \(p\)-adic wavelets and their applications ⋮ Non-Haar \(p\)-adic wavelets and pseudodifferential operators ⋮ On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over \(p\)-adic field ⋮ \(p\)-adic refinable functions and MRA-based wavelets ⋮ Non-Haar \(p\)-adic wavelets and their application to pseudo-differential operators and equations

Cites Work

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• Localization in space for a free particle in ultrametric quantum mechanics
• p-adic quantum mechanics
• Harmonic analysis in the \(p\)-adic Lizorkin spaces: Fractional operators, pseudo-differential equations, \(p\)-adic wavelets, Tauberian theorems
• Harmonic analysis on \(n\)-dimensional vector spaces over local fields. I: Basic results on fractional integration
• p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes
• Pseudo-Differential Operators in the p-Adic Lizorkin Space

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