Multidimensional nonlinear pseudo-differential evolution equation with \(p\)-adic spatial variables

DOI10.1007/s11868-019-00320-3zbMath1454.35423arXiv1909.06758OpenAlexW2996418123WikidataQ115377541 ScholiaQ115377541MaRDI QIDQ2174860

Anatoly N. Kochubei, Alexandra Vict. Antoniouk, Andrei Yu. Khrennikov

Publication date: 27 April 2020

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.06758

zbMATH Keywords

Markov processmild solutionporous medium equation\(p\)-adic numbersm-accretive operatorVladimirov's fractional differentiation

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Nonlinear evolution equations (47J35) Initial value problems for PDEs with pseudodifferential operators (35S10) Fractional partial differential equations (35R11)

Related Items (9)

Some further classes of pseudo-differential operators in the \(p\)-adic context and their applications ⋮ New classes of parabolic pseudo-differential equations, Feller semigroups, contraction semigroups and stochastic process on the \(p\)-adic numbers ⋮ Heat equations and wavelets on Mumford curves and their finite quotients ⋮ Commutators of Hardy-Littlewood operators on \(p\)-adic function spaces with variable exponents ⋮ Solving nonlinear \(p\)-adic pseudo-differential equations: combining the wavelet basis with the Schauder fixed point theorem ⋮ Reaction-diffusion equations on complex networks and Turing patterns, via \(p\)-adic analysis ⋮ New classes of \(p\)-adic evolution equations and their applications ⋮ Components and exit times of Brownian motion in two or more \(p\)-adic dimensions ⋮ Non-Archimedean pseudo-differential operators on Sobolev spaces related to negative definite functions

Cites Work

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• Pseudodifferential equations over non-Archimedean spaces
• Tables of integrals for complex-valued functions of \(p\)-adic arguments
• Toward an ultrametric theory of turbulence
• Regularizing effects for \(u_ t\) + A phi(u) = 0 in \(L^ 1\).
• \(p\)-adic analogue of the porous medium equation
• Local properties of Lévy processes on a totally disconnected group
• Semi-linear second-order elliptic equations in \(L^1\)
• Methods and applications of ultrametric and \(p\)-adic analysis: from wavelet theory to biophysics
• Isotropic Markov semigroups on ultra-metric spaces
• Fourier Analysis on Local Fields. (MN-15)
• p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes
• Application ofp-adic analysis to models of breaking of replica symmetry
• Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems
• p-Adic Models of Turbulence
• Nonlinear Differential Equations of Monotone Types in Banach Spaces

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