23 citations · 59 across the 25 of their papers we have counts for
9 papers · 1 filter
On operator estimates in homogenization of non-local operators of convolution type
A. Piatnitski, V. Sloushch, T. Suslina +1
The paper studies a bounded symmetric operator in with $$ ({\mathbf{A}}_\varepsilon u) (x) = \varepsilon^{-d-2} \int_{\mathbf{R}^d} a…
Mathematical multi-scale model of water purification
A. Piatnitski, A. Shamaev, E. Zhizhina
In this work we consider a mathematical model of the water treatment process and determine the effective characteristics of this model. At the microscopic length scale we describe…
Invariant measures for spatial contact model in small dimensions
Yuri Kondratiev, Oleksandr Kutoviy, Sergey Pirogov +1
We study invariant measures of continuous contact model in small dimensional spaces (). Under general conditions we prove that in the critical regime this system has the on…
Resolvent bounds for jump generators and ground state asymptotics for nonlocal Schrödinger operators
Yuri Kondratiev, Stanislav Molchanov, Andrey Piatnitski +1
The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially we prove a number of lower and upper bounds for…
A quasispecies continuous contact model in a critical regime
Yuri Kondratiev, Sergey Pirogov, Elena Zhizhina
We study a new non-equilibrium dynamical model: a marked continuous contact model in -dimensional space (). We prove that for certain values of rates (the critical regi…
On ground state of non local Schrodinger operators
Yuri Kondratiev, Stanislav Molchanov, Sergey Pirogov +1
We study a ground state of a non local Schrodinger operator associated with an evolution equation for the density of population in the stochastic contact model in continuum with in…