Development of methods of asymptotic analysis of transition layers in reaction–diffusion–advection equations: Theory and applications

NN Nefedov - Computational Mathematics and Mathematical Physics, 2021 - Springer
This work presents a review and analysis of modern asymptotic methods for analysis of
singularly perturbed problems with interior and boundary layers. The central part of the work …

Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front

DV Lukyanenko, AA Borzunov… - … in nonlinear science and …, 2021 - Elsevier
An approach to solving coefficient inverse problems for nonlinear reaction-diffusion-
advection equations is proposed. As an example, we consider an inverse problem of …

CPU-time and RAM memory optimization for solving dynamic inverse problems using gradient-based approach

DV Klyuchinskiy, NS Novikov, MA Shishlenin - Journal of Computational …, 2021 - Elsevier
Numerical solution of inverse problem for 2D acoustic system of conservation laws by
gradient type method requires storage of O (N 3) elements which is crucial on large grids …

Inverse problem of recovering the initial condition for a nonlinear equation of the reaction–diffusion–advection type by data given on the position of a reaction front with …

D Lukyanenko, T Yeleskina, I Prigorniy, T Isaev… - Mathematics, 2021 - mdpi.com
In this paper, approaches to the numerical recovering of the initial condition in the inverse
problem for a nonlinear singularly perturbed reaction–diffusion–advection equation are …

The problem of the non-uniqueness of the solution to the inverse problem of recovering the symmetric states of a bistable medium with data on the position of an …

N Levashova, A Gorbachev, R Argun, D Lukyanenko - Symmetry, 2021 - mdpi.com
The paper considers the question of the possibility of recovering symmetric stable states of a
bistable medium in the inverse problem for a nonlinear singularly perturbed autowave …

Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms

X Wu, M Ni - Communications in Nonlinear Science and Numerical …, 2020 - Elsevier
In this project, we study the periodic Dirichlet boundary value problem for a singularly
perturbed reaction-advection-diffusion equation on the segment in case of discontinuous …

Convergence analysis for forward and inverse problems in singularly perturbed time-dependent reaction-advection-diffusion equations

D Chaikovskii, Y Zhang - Journal of Computational Physics, 2022 - Elsevier
In this paper, by employing the asymptotic expansion method, we prove the existence and
uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed …

Some features of solving an inverse backward problem for a generalized Burgers' equation

DV Lukyanenko, IV Prigorniy… - Journal of Inverse and Ill …, 2020 - degruyter.com
In this paper, we consider an inverse backward problem for a nonlinear singularly perturbed
parabolic equation of the Burgers' type. We demonstrate how a method of asymptotic …

Use of asymptotic analysis for solving the inverse problem of source parameters determination of nitrogen oxide emission in the atmosphere

SA Zakharova, MA Davydova… - Inverse Problems in …, 2021 - Taylor & Francis
The possibilities of using asymptotic analysis for solving the inverse problem of restoring the
parameters of the source of nitrogen oxide industrial emissions into the atmosphere are …

Application of a numerical-asymptotic approach to the problem of restoring the parameters of a local stationary source of anthropogenic pollution

MA Davydova, NF Elansky, SA Zakharova… - Doklady …, 2021 - Springer
A numerical-asymptotic approach is used to solve some coefficient inverse problems of
tracer diffusion in the atmosphere. An asymptotic solution of the direct problem for an …