Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction-diffusion problem
DOI10.1016/j.cam.2022.114294zbMath1490.35024OpenAlexW4226416379MaRDI QIDQ2141591
Dmitry V. Lukyanenko, V. T. Volkov, R. L. Argun
Publication date: 25 May 2022
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2022.114294
blow-upsingularly perturbed problemmodel reductionreaction-diffusion equationcombination of asymptotic and numerical approachesmoving transition layers
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Asymptotic expansions of solutions to PDEs (35C20) Blow-up in context of PDEs (35B44)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Blow-up for one Sobolev problem: theoretical approach and numerical analysis
- A numerical method for a nonlinear singularly perturbed interior layer problem using an approximate layer location
- An efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers
- On numerical modelling and the blow-up behavior of contact lines with a \(180\degree\) contact angle
- A brief survey on numerical methods for solving singularly perturbed problems
- Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems
- Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem
- Green's function estimates for a singularly perturbed convection-diffusion problem
- Contrast structures in problems for a stationary equation of reaction-diffusion-advection type with discontinuous nonlinearity
- A coupled system of singularly perturbed parabolic reaction-diffusion equations
- Identification of nonlinear heat conduction laws
- An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas
- Blow up of incompressible Euler solutions
- A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain
- Singularly perturbed parabolic problems with non-smooth data.
- Mathematical biology. Vol. 1: An introduction.
- Asymptotic behavior of solutions of the Cauchy problem for Burgers type equations
- On a set of singularly perturbed convection--diffusion equations
- Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
- Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions
- Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation
- Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front
- Approximate solution of inverse problems for the heat equation with a singular perturbation
- 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
- Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms
- Singularly perturbed reaction-diffusion problems with discontinuities in the initial and/or the boundary data
- Algorithm for determining the volatility function in the Black-Scholes model
- 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
- Contrast structure for singular singularly perturbed boundary value problem
- Estimates for solutions of Burgers type equations and some applications
- Numerical diagnosis of blow-up of solutions of pseudoparabolic equations
- Front motion in the parabolic reaction-diffusion problem
- Robust Numerical Methods for Singularly Perturbed Differential Equations
- Numerical Analysis of a 2d Singularly Perturbed Semilinear Reaction-Diffusion Problem
- Third-order nonlinear dispersive equations: Shocks, rarefaction, and blowup waves
- A rescaling algorithm for the numerical calculation of blowing-up solutions
- Some general implicit processes for the numerical solution of differential equations
- Recovering a Time-Dependent Diffusion Coefficient from Nonlocal Data
- A regularizing Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography
- A Class of Singularly Perturbed Convection-Diffusion Problems with a Moving Interior Layer. An a Posteriori Adaptive Mesh Technique
- Blow‐up for Joseph–Egri equation: Theoretical approach and numerical analysis
- An adjoint method in inverse problems of chromatography