A new class of multi-scale reaction-diffusion systems with closed-form, low-dimensional, invariant manifolds
DOI10.1090/conm/806/16156MaRDI QIDQ6630002
Publication date: 30 October 2024
model reductionMichaelis-Menten modelDavis-Skodje modellow-dimensional invariant manifoldsmulti-scale partial differential equations
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Multiple scale methods for ordinary differential equations (34E13) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A constructive approach to quasi-steady state reductions
- Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
- Entropy-related extremum principles for model reduction of dissipative dynamical systems
- Second-order splitting schemes for a class of reactive systems
- Approximately invariant manifolds and global dynamics of spike states
- Inertial manifolds for nonlinear evolutionary equations
- Quasi-steady-state approximation for chemical reaction networks
- Infinite-dimensional dynamical systems in mechanics and physics
- Singular perturbation methods for ordinary differential equations
- Asymptotic analysis of two reduction methods for systems of chemical reactions
- Mathematical biology. Vol. 1: An introduction.
- Classical quasi-steady state reduction -- a mathematical characterization
- Analysis of the approximate slow invariant manifold method for reactive flow equations
- Invariant manifolds for physical and chemical kinetics
- Computing inertial manifolds
- Analysis of the computational singular perturbation reduction method for chemical kinetics
- The use of algebraic sets in the approximation of inertial manifolds and lumping in chemical kinetic systems
- On the influence of cross-diffusion in pattern formation
- Slow manifolds for infinite-dimensional evolution equations
- Determining ``small parameters for quasi-steady state
- Diffusion and cross-diffusion in pattern formation
- Instability induced by cross-diffusion in reaction-diffusion systems
- One-Dimensional Slow Invariant Manifolds for Fully Coupled Reaction and Micro-scale Diffusion
- Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions
- Geometry of the Computational Singular Perturbation Method
- Existence and persistence of invariant manifolds for semiflows in Banach space
- Asymptotic Solution of Stiff PDEs with the CSP Method: The Reaction Diffusion Equation
- Stability estimates for systems with small cross-diffusion
- The Utility of an Invariant Manifold Description of the Evolution of a Dynamical System
- The Quasi-Steady-State Assumption: A Case Study in Perturbation
- Computational Singular Perturbation Method for Nonstandard Slow-Fast Systems
- Geometric Singular Perturbation Theory Beyond the Standard Form
- The boundedness-by-entropy method for cross-diffusion systems
- The extension of the ILDM concept to reaction–diffusion manifolds
- Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes
This page was built for publication: A new class of multi-scale reaction-diffusion systems with closed-form, low-dimensional, invariant manifolds
