Related papers: Fast Reactions and Slow Manifolds
Multiple time scales problems are investigated by combining geometrical and analytical approaches. More precisely, for fast-slow reaction-diffusion systems, we first prove the existence of slow manifolds for the abstract problem under the…
The aim of this expository paper is twofold. We start with a concise overview of the theory of invariant slow manifolds for fast-slow dynamical systems starting with the work by Tikhonov and Fenichel to the most recent works on…
We extend classical finite-dimensional Fenichel theory in two directions to infinite dimensions. Under comparably weak assumptions we show that the solution of an infinite-dimensional fast-slow system is approximated well by the…
We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and…
The fast-reaction limit for reaction--diffusion systems modelling predator--prey interactions is investigated. In the considered model, predators exist in two possible states, namely searching and handling. The switching rate between these…
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models…
We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and…
In this paper we study a family of semilinear reaction-diffusion equations on thin spatial domains, lying close to a lower dimensional submanifold $M$. As the thickness tends to zero, the domains collapse onto (a subset of) $M$. As it was…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
The classical Chapman-Enskog procedure admits a substantial geometrical generalization known as slow manifold reduction. This generalization provides a paradigm for deriving and understanding most reduced models in plasma physics that are…
In this paper, we present an approach to characterising self-similar fast-reaction limits of systems with nonlinear diffusion. For appropriate initial data, in the fast-reaction limit as k tends to infinithy,spatial segregation results in…
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
In this paper, we present an approach to characterising fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential…
The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity at infinity of the Poincar\'e-Lyapunov sphere for slow-fast…
The estimation of the kinetic parameters requires the careful design of experiments under a constrained set of conditions. Many estimates reported in the literature incorporate protocols that leverage simplified mathematical models known as…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
Chemical kinetic models in terms of ordinary differential equations correspond to finite dimensional dissipative dynamical systems involving a multiple time scale structure. Most dimension reduction approaches aimed at a slow…
The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis--Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation…
Model reduction of fast-slow chemical reaction networks based on the quasi-steady state approximation fails when the fast subsystem has first integrals. We call these first integrals approximate conservation laws. In order to define fast…