arXiv subjects

A. Pogorui

Publications and source records attributed to A. Pogorui.

3 recordsLinked to original sources

arXiv2019

An algebraic approach for solving fourth-order partial differential equations

It is well-known that any solution of the Laplace equation is a real or imaginary part of a complex holomorphic function. In this paper, in some sense, we extend this property into four order hyperbolic and elliptic type PDEs. To be more specific, the extension is for a $c$-biwave PDE with constant coefficients, and we show that the components of a differentiable function on the associated hypercomplex algebras provide solutions for the equation.

math.AP↗

arXiv2012

The Distribution of Random Evolution in Erlang Semi-Marov Media

In this paper we study a one-dimensional random motion by having a general Erlang distribution for the sojourn times of the switching process and we obtain solution of the four order hyperbolic PDE for 2-Erlang case.

math.PR↗

arXiv2012

Asymptotic Expansion for Distribution of Markovian Random Motion

In this paper we study an asymptotic expansion for the distribution of a random motion of a particle driven by a Markov process in diffusion approximation. We show that the singularly perturbed equation of a Markovian random motion can be reduced to the regularly perturbed equation for the distribution of the random motion.

math.PR↗