Inverse problems for the nonlinear modified transfer equation

TL;DR

This paper investigates inverse problems for a nonlinear modified transfer equation, extending previous linear models by incorporating nonlinear factors in absorption or scattering, and explores their solvability and properties.

Contribution

It introduces a new approach to inverse problems for nonlinear modified transfer equations, building on prior linear models and addressing nonlinear complexities.

Findings

Established conditions for solvability of inverse problems

Extended existing models to include nonlinear modifications

Provided theoretical analysis of solution properties

Abstract

This article is devoted to inverse problems for nonlinear equations of the modified transfer, which can be regarded as a manageable problem. Various productions such problems for normal (unmodified) of the transport equation studied earlier by A.I. Prilepko and most complete form in the dissertation of his follower N. Volkov. If management is a factor in the coefficient of absorption or scattering indicatrix, even in the case of conventional linear transfer equation inverse problem become nonlinear (in the thesis N. P. Volkov overcome this difficulty). The paper deals with modification of the transport equation (for Similar to the way it is done Ozeen for the Navier - Stokes equations)