5 citations · 6 across the 6 of their papers we have counts for
7 papers
Non-Archimedean Kelvin Transformation
Alexandra V. Antoniouk, Anatoly N. Kochubei
We introduce and study an analog of the Kelvin transformation connected with the Vladimirov-Taibleson operator acting on real- or complex-valued functions on a space over a n…
Non-Archimedean Neumann problem: weak and strong solutions
Alexandra V. Antoniouk, Anatoly N. Kochubei
We consider the Neumann problem for the equation with the Vladimirov-Taibleson fractional differentiation operator over a non-Archimedean local field. We study weak solutions follo…
Existence and uniqueness for -adic counterpart of the porous medium equation
Alexandra Antoniouk, Anatoly Kochubei, Oleksii Nikitchenko
We develop a theory of generalized solutions of the nonlinear evolution equations for complex-valued functions of a real positive time variable and -adic spatial variable, which…
Decay of correlations and uniqueness of Gibbs lattice systems with non-quadratic interaction
Alexander Val. Antoniouk, Alexandra Vict. Antoniouk
We aim this paper to develop the classical lattice models with unbounded spin to the case of non-quadratic polynomial interaction. We demonstrate that the distinct relation between…
Multidimensional nonlinear pseudo-differential evolution equation with p-adic spatial variables
Alexandra V. Antoniouk, Andrei Yu. Khrennikov, Anatoly N. Kochubei
We study the Cauchy problem for -adic nonlinear evolutionary pseudo-differential equations for complex-valued functions of a real positive time variable and p-adic spatial varia…
Variational principle for weighted porous media equation
Alexandra Antoniouk, Marc Arnaudon
In this paper we state the variational principle for the weighted porous media equation. It extends V.I. Arnold's approach to the description of Euler flows as a geodesics on some…
Generalized Navier-Stokes flows and applications to incompressible viscous fluids
Alexandra Antoniouk, Marc Arnaudon, Ana Bela Cruzeiro
We introduce a notion of generalized stochastic flows on mani- folds, that extends to the viscous case the one defined by Brenier for perfect fluids. Their kinetic energy extends t…