A. V. Kalinin, A. A. Tyukhtina, “On a nonlinear problem for a system of integro-differential equations of radiative transfer theory”, Zh. Vychisl. Mat. Mat. Fiz., 2022, Volume 62, Number 6,Pages <nobr>965

This article is cited in 2 papers

Partial Differential Equations

On a nonlinear problem for a system of integro-differential equations of radiative transfer theory

A. V. Kalinin^ab, A. A. Tyukhtina^a

^a Lobachevsky University of Nizhny Novgorod, 603022, Nizhny Novgorod, Russia
^b Institute of Applied Physics, Russian Academy of Sciences, 603950, Nizhny Novgorod, Russia

Abstract: An initial-boundary value problem for a system of nonlinear integro-differential equations of radiative transfer theory is considered. An existence and uniqueness theorem for this problem is proved. Based on the properties of semigroups of isotone operators acting in conditionally complete lattices, stabilization of the solution of the problem as $t\to\infty$ is established.

Key words: system of radiative transfer equations, nonlinear integro-differential equations, semigroups of isotone operators.

UDC: 517.95

Received: 12.12.2021
Revised: 20.01.2022
Accepted: 11.02.2022

DOI: 10.31857/S0044466922060102