Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

VG Sorokin, AV Vyazmin - Mathematics, 2022 - mdpi.com
The paper describes essential reaction–diffusion models with delay arising in population
theory, medicine, epidemiology, biology, chemistry, control theory, and the mathematical …

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 …

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 …

A modified liu and storey conjugate gradient method for large scale unconstrained optimization problems

Z Salleh, G Alhamzi, I Masmali, A Alhawarat - Algorithms, 2021 - mdpi.com
The conjugate gradient method is one of the most popular methods to solve large-scale
unconstrained optimization problems since it does not require the second derivative, such …

Multidimensional thermal structures in the singularly perturbed stationary models of heat and mass transfer with a nonlinear thermal diffusion coefficient

MA Davydova, SA Zakharova - Journal of Computational and Applied …, 2022 - Elsevier
A new approach to the study of multidimensional singularly perturbed problems of nonlinear
heat conduction is proposed, based on the further development and use of asymptotic …

On some features of the numerical solving of coefficient inverse problems for an equation of the reaction-diffusion-advection-type with data on the position of a reaction …

R Argun, A Gorbachev, D Lukyanenko, M Shishlenin - Mathematics, 2021 - mdpi.com
The work continues a series of articles devoted to the peculiarities of solving coefficient
inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion …

On estimation of the contribution of secondary vortex structures to the transport of aerosols in the atmospheric boundary layer

MA Davydova, OG Chkhetiani, NT Levashova… - Fluid Dynamics, 2022 - Springer
In this paper, we consider two reasonable approaches to the problem of numerical
simulation of the concentration distribution of a finely dispersed aerosol in spiral vortex …

Inverse problem for an equation of the reaction-diffusion-advection type with data on the position of a reaction front: features of the solution in the case of a nonlinear …

R Argun, A Gorbachev, N Levashova, D Lukyanenko - Mathematics, 2021 - mdpi.com
The paper considers the features of numerical reconstruction of the advection coefficient
when solving the coefficient inverse problem for a nonlinear singularly perturbed equation of …

Iterative methods for Navier-Stokes inverse problems

L O'Connor, D Lecoanet, EH Anders, KC Augustson… - Physical Review E, 2024 - APS
Even when the partial differential equation underlying a physical process can be evolved
forward in time, the retrospective (backward in time) inverse problem often has its own …

Estimating adsorption isotherm parameters in chromatography via a virtual injection promoting double feed-forward neural network

C Xu, Y Zhang - Journal of Inverse and Ill-posed Problems, 2022 - degruyter.com
The means to obtain the adsorption isotherms is a fundamental open problem in competitive
chromatography. A modern technique of estimating adsorption isotherms is to solve a …