The Cauchy problems for evolutionary pseudo-differential equations over \(p\)-adic field and the wavelet theory

DOI10.1016/j.jmaa.2010.08.053zbMath1218.47071OpenAlexW1591297299MaRDI QIDQ616692

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

Publication date: 12 January 2011

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.08.053

zbMATH Keywords

fractional operator\(p\)-adic waveletsvariable separation method\(p\)-adic Lizorkin space\(p\)-adic pseudo-differential equation\(p\)-adic pseudo-differential operator

Mathematics Subject Classification ID

Related Items (19)

Application of \(p\)-adic wavelets to model reaction-diffusion dynamics in random porous media ⋮ \(p\)-adic mathematical physics: the first 30 years ⋮ Wavelet analysis on adeles and pseudo-differential operators ⋮ Solving nonlinear \(p\)-adic pseudo-differential equations: combining the wavelet basis with the Schauder fixed point theorem ⋮ Applications of \(p\)-adics to geophysics: linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions ⋮ Random processes on non-Archimedean spaces ⋮ Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity ⋮ Multiresolution analysis on product of zero-dimensional Abelian groups ⋮ The 2-adic derivatives and fractal dimension of Takagi-like function on 2-series field ⋮ Adelic multiresolution analysis, construction of wavelet bases and pseudo-differential operators ⋮ Step refinable functions and orthogonal MRA on Vilenkin groups ⋮ Matrix model for Riemann zeta via its local factors ⋮ Enhanced symmetry of the \(p\)-adic wavelets ⋮ APPLICATION OF p-ADIC ANALYSIS TO TIME SERIES ⋮ \(p\)-adic analogue of the porous medium equation ⋮ Pseudodifferential operators on \({\mathbb{Q}_p}\) and \(L\)-series ⋮ On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over \(p\)-adic field ⋮ \(p\)-adic analogue of the wave equation ⋮ Local well-posedness of the Cauchy problem for a \(p\)-adic Nagumo-type equation

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