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

DOI10.1515/jiip-2017-0074zbMath1430.35269OpenAlexW2963694293WikidataQ127487374 ScholiaQ127487374MaRDI QIDQ2010475

Dmitry V. Lukyanenko, V. T. Volkov, Maxim A. Shishlenin

Publication date: 27 November 2019

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip-2017-0074

zbMATH Keywords

numerical methodsingularly perturbed probleminverse boundary value problemreaction-diffusion-advection equationinterior layers

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Inverse problems in optimal control (49N45) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Numerical solution to inverse problems in abstract spaces (65J22) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Related Items

CPU-time and RAM memory optimization for solving dynamic inverse problems using gradient-based approach, Features of numerical reconstruction of a boundary condition in an inverse problem for a reaction-diffusion-advection equation with data on the position of a reaction front, Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction-diffusion problem, Asymptotic solution of the inverse problem for restoring the modular type source in Burgers' equation with modular advection, Some features of solving an inverse backward problem for a generalized Burgers' equation, Asymptotically stable stationary solutions of the reaction-diffusion-advection equation with discontinuous reaction and advection terms, Stability of a stationary solution of a system of activator-inhibitor-type equations with a double-scale internal transition layer, Approximation of the solution of an inverse problem for a singularly perturbed system of partial differential equations, Approximate solution of an inverse problem for a singularly perturbed integro-differential heat equation, On an inverse problem for a linearized system of Navier-Stokes equations with a final overdetermination condition, On the features of numerical solution of coefficient inverse problems for nonlinear equations of the reaction-diffusion-advection type with data of various types, Asymptotic solution of coefficient inverse problems for Burgers-type equations, Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms, Use of asymptotic analysis for solving the inverse problem of source parameters determination of nitrogen oxide emission in the atmosphere, Application of a numerical-asymptotic approach to the problem of restoring the parameters of a local stationary source of anthropogenic pollution, Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front, Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics, Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications, Convergence analysis for forward and inverse problems in singularly perturbed time-dependent reaction-advection-diffusion equations, Asymptotic solution of the boundary control problem for a Burgers-type equation with modular advection and linear gain

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of an inverse problem of coefficient recovering for a wave equation by a stochastic projection methods
• Identification of nonlinear heat conduction laws
• Numerical solution of the multidimensional Gelfand-Levitan equation
• Fast Toeplitz linear system inversion for solving two-dimensional acoustic inverse problem
• An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas
• Boundary control, wave field continuation and inverse problems for the wave equation
• Variational approach to the study of processes of geophysical hydro-thermodynamics with assimilation of observation data
• PDE-constrained optimization in medical image analysis
• Solving of the coefficient inverse problem for a nonlinear singularly perturbed two-dimensional reaction-diffusion equation with the location of moving front data
• Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data
• Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations
• Analytical-numerical approach to describing time-periodic motion of fronts in singularly perturbed reaction-advection-diffusion models
• Analysis and numerical solution of coupled volume-surface reaction-diffusion systems with application to cell biology
• Numerical algorithm for two-dimensional inverse acoustic problem based on Gel'fand–Levitan–Krein equation
• Definitions and examples of inverse and ill-posed problems
• Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem
• New Schemes for Differential-Algebraic Stiff Systems
• Some general implicit processes for the numerical solution of differential equations
• To the reconstruction of a riemannian manifold via its spectral data (Bc–Method)
• Boundary control in reconstruction of manifolds and metrics (the BC method)
• Inverse acoustic problems: theory and numerical methods
• Recovering a Time-Dependent Diffusion Coefficient from Nonlocal Data
• Boundary control and Gel'fand–Levitan–Krein methods in inverse acoustic problem
• A Globally Convergent Numerical Method for a Coefficient Inverse Problem
• Imaging of Buried Objects from Experimental Backscattering Time-Dependent Measurements Using a Globally Convergent Inverse Algorithm
• Use of Asymptotics for New Dynamic Adapted Mesh Construction for Periodic Solutions with an Interior Layer of Reaction-Diffusion-Advection Equations
• Front Dynamics in an Activator-Inhibitor System of Equations
• Asymptotic-Numerical Method for the Location and Dynamics of Internal Layers in Singular Perturbed Parabolic Problems
• A globally accelerated numerical method for optical tomography with continuous wave source