\(p\)-adic analogue of the wave equation

DOI10.1007/s00041-019-09668-yzbMath1473.35674OpenAlexW2913597697MaRDI QIDQ2326869

Bo Wu, Andrei Yu. Khrennikov

Publication date: 10 October 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-019-09668-y

zbMATH Keywords

Cauchy problemregularized solution\(p\)-adic elliptic equation

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) (p)-adic differential equations (12H25) Non-Archimedean function theory (30G06) Initial value problems for PDEs with pseudodifferential operators (35S10) (p)-adic and power series fields (11D88) Fractional partial differential equations (35R11)

Related Items (3)

p-Adic Wave Equations on Finite Graphs and T 0-Spaces ⋮ Non-Archimedean radial calculus: Volterra operator and Laplace transform ⋮ On the p-Adic analog of Richards’ equation with the finite difference method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Application of \(p\)-adic wavelets to model reaction-diffusion dynamics in random porous media
• Parabolic type equations and Markov stochastic processes on adeles
• Adelic multiresolution analysis, construction of wavelet bases and pseudo-differential operators
• A note on a Cauchy problem for the Laplace equation: Regularization and error estimates
• The Cauchy problems for evolutionary pseudo-differential equations over \(p\)-adic field and the wavelet theory
• A non-Archimedean wave equation
• Non-Haar \(p\)-adic wavelets and their application to pseudo-differential operators and equations
• p-adic space-time and string theory
• Pseudo-differential operators and derivatives on locally compact Vilenkin groups
• \(p\)-adic analogue of the porous medium equation
• The Cauchy problem of coupled elliptic sine-Gordon equations with noise: analysis of a general kernel-based regularization and reliable tools of computing
• Regularity bounds for a Gevrey criterion in a kernel-based regularization of the Cauchy problem of elliptic equations
• The Cauchy problem for a class of pseudodifferential equations over \(p\)-adic field
• Two regularization methods for a Cauchy problem for the Laplace equation
• Parabolic equations and Markov processes over \(p\)-adic fields
• Harmonic analysis in the \(p\)-adic Lizorkin spaces: Fractional operators, pseudo-differential equations, \(p\)-adic wavelets, Tauberian theorems
• Fundamental solutions of pseudo-differential operators over \(p\)-adic fields
• \(p\)-adic pseudodifferential operators and \(p\)-adic wavelets
• ADELIC HARMONIC OSCILLATOR
• Wavelets and spectral analysis of ultrametric pseudodifferential operators
• A note on differential operators on finite non-abelian groups
• Generalized functions over the field ofp-adic numbers
• Fourier Analysis on Local Fields. (MN-15)
• Ultrametric Pseudodifferential Equations and Applications
• Wavelet theory as $ p$-adic spectral analysis
• Pseudo-differential operators over <italic>p</italic>-adic fields
• Walsh-fourier series and the concept of a derivative^†

This page was built for publication: \(p\)-adic analogue of the wave equation