Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation

DV Lukyanenko, MA Shishlenin… - Journal of Inverse and Ill …, 2019 - degruyter.com
In this paper, a new asymptotic-numerical approach to solving an inverse boundary value
problem for a nonlinear singularly perturbed parabolic equation with time-periodic …

[HTML][HTML] Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction–diffusion equation with the location of moving front …

DV Lukyanenko, VB Grigorev, VT Volkov… - … & Mathematics with …, 2019 - Elsevier
Asymptotic-numerical approach to solving the coefficient inverse problem for a nonlinear
singularly perturbed two-dimensional reaction–diffusion equation by knowing the location of …

Asymptotic solution of coefficient inverse problems for Burgers-type equations

VT Volkov, NN Nefedov - Computational Mathematics and Mathematical …, 2020 - Springer
For a singularly perturbed reaction–diffusion–advection equation, called in applications a
Burgers-type equation and having a time-periodic solution with an internal transition layer …

Asymptotic solution of the inverse problem for restoring the modular type source in Burgers' equation with modular advection

NN Nefedov, VT Volkov - Journal of Inverse and Ill-posed Problems, 2020 - degruyter.com
For a singularly perturbed Burgers' type equation with modular advection that has a time-
periodic solution with an internal transition layer, asymptotic analysis is applied to solve the …

Application of asymptotic analysis for solving the inverse problem of determining the coefficient of linear amplification in Burgers' equation

DV Lukyanenko, VT Volkov, NN Nefedov… - Moscow University …, 2019 - Springer
Asymptotic analysis of a singularly perturbed reaction—diffusion—advection equation,
which is called a Burgers-type equation in applications and has a solution with a sharp …

Asymptotic approximation of the solution of the reaction-diffusion-advection equation with a nonlinear advective term

EA Antipov, NT Levashova… - Modeling and Analysis of …, 2018 - mais-journal.ru
We consider a solution in a moving front form of the initial-boundary value problem for a
singularly perturbed reaction-diffusion equation in a band with periodic conditions in one of …

Solving forward and inverse problems involving a nonlinear three-dimensional partial differential equation via asymptotic expansions

D Chaikovskii, Y Zhang - IMA Journal of Applied Mathematics, 2023 - academic.oup.com
This paper concerns the use of asymptotic expansions for the efficient solving of forward and
inverse problems involving a nonlinear singularly perturbed time-dependent reaction …

Solving forward and inverse problems in a non-linear 3D PDE via an asymptotic expansion based approach

D Chaikovskii, Y Zhang - arXiv preprint arXiv:2210.05220, 2022 - arxiv.org
This paper concerns the use of asymptotic expansions for the efficient solving of forward and
inverse problems involving a nonlinear singularly perturbed time-dependent reaction …

On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types

DV Lukyanenko, RL Argun, AA Borzunov… - Differential …, 2023 - Springer
The paper discusses the features of constructing numerical schemes for solving coefficient
inverse problems for nonlinear partial differential equations of the reaction–diffusion …

Асимптотическое решение коэффициентных обратных задач для уравнений типа Бюргерса

ВТ Волков, НН Нефедов - Журнал вычислительной математики и …, 2020 - elibrary.ru
Для сингулярно возмущенного уравнения реакция-диффузия-адвекция, называемого в
приложениях уравнением типа Бюргерса и имеющего периодическое по времени …