Singular perturbation analysis of a stationary diffusion/reaction system whose solution exhibits a corner-type behavior in the interior of the domain
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TLDR
In this article, a singularly perturbed system of second-order differential equations describing steady state of a chemical process was considered, and a formal asymptotic expansion of the solution was constructed in the case when solution exhibits a corner-type behavior.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2003-12-15 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Method of matched asymptotic expansions & Singular perturbation.read more
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Numerical exploration of a system of reaction–diffusion equations with internal and transient layers
TL;DR: In this paper, a reaction pathway for a classical two-species reaction with one reaction that is several orders of magnitudes faster than the other is considered, and the results of exploratory numerical simulations are designed to provide guidance for the analysis to be performed for the transient problem.
Singularly perturbed boundary value problems in case of exchange of stablities
TL;DR: In this paper, a mixed boundary value problem for a system of two second-order nonlinear differential equations where one equation is singularly perturbed is considered, and the authors prove the existence of a solution of the problem and determine its asymptotic behavior with respect to the small parameter.
Journal ArticleDOI
One-Dimensional Slow Invariant Manifolds for Fully Coupled Reaction and Micro-scale Diffusion
TL;DR: The method of slow invariant manifolds, applied previously to model the reduced kinetics of spatially homogeneous reactive systems, is extended to systems with diffusion by identifying steady state solutions to the governing partial differential equations and connecting analogous orbits in the Galerkin-projected space.
Journal ArticleDOI
Interface conditions for a singular reaction-diffusion system
TL;DR: In this article, a chemical reaction/diffusion system, a very fast reaction $A+B+C$ to C$ ✓ ✓ ✓ denotes non-coexistence of the resulting interfaces.
Journal Article
Non-Linear Reaction-Diffusion Process in a Thin Membrane and Homotopy Analysis Method
TL;DR: In this paper, a closed form of an analytical expression of concentrations for the full range of enzyme activities has been derived using Homotopy analysis method, which is compared with the numerical results.
References
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Book
Maximum principles in differential equations
TL;DR: The One-Dimensional Maximum Principle (MDP) as mentioned in this paper is a generalization of the one-dimensional maximum principle (OMP) for the construction of hyperbolic equations.
MonographDOI
The Boundary Function Method for Singular Perturbation Problems
TL;DR: In this article, the boundary function method has been applied in the theory of semiconductor devices, and a mathematical model of combustion process in the case of autocatalytic reaction has been proposed.
Journal ArticleDOI
A One-Dimensional Reaction/Diffusion System with a Fast Reaction☆
TL;DR: In this article, the authors considered a system of second-order ODEs describing steady state for a three-component chemical system with diffusion, where one of the reactions is fast and discussed the existence of solutions and the uniqueness and characterization of a limit as the rate of the fast reaction approaches infinity.
Journal ArticleDOI
Singularly Perturbed Boundary Value Problems in Case of Exchange of Stabilities
TL;DR: In this paper, a mixed boundary value problem for a system of two second-order nonlinear differential equations where one equation is singularly perturbed is considered, and the authors prove the existence of a solution of the problem and determine its asymptotic behavior with respect to the small parameter.
Singularly perturbed boundary value problems in case of exchange of stablities
TL;DR: In this paper, a mixed boundary value problem for a system of two second-order nonlinear differential equations where one equation is singularly perturbed is considered, and the authors prove the existence of a solution of the problem and determine its asymptotic behavior with respect to the small parameter.