Geometric analysis of a truncated Galerkin discretization of fast-slow PDEs with transcritical singularities
DOI10.1137/23M1572702MaRDI QIDQ6661624
Maximilian Engel, Christian Kuehn
Publication date: 13 January 2025
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
invariant manifoldsreaction-diffusion equationsslow manifoldspectral Galerkin approximationblow-up methodloss of normal hyperbolicity
Reaction-diffusion equations (35K57) Bifurcations of singular points in dynamical systems (37G10) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65) Singular perturbations for ordinary differential equations (34E15)
Cites Work
- Title not available (Why is that?)
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- Multiple time scale dynamics
- Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
- Resolution of singularities of real-analytic vector fields in dimension three
- Approximately invariant manifolds and global dynamics of spike states
- Mathematical foundations of neuroscience
- Geometric theory of semilinear parabolic equations
- Geometric singular perturbation theory for ordinary differential equations
- Duck-shaped solutions and winding.
- Manifolds, tensor analysis, and applications.
- Infinite-dimensional dynamical systems in mechanics and physics.
- Bifurcation theory. An introduction with applications of PDEs
- Singularly perturbed boundary value problems for systems of Tichonov's type in case of exchange of stabilities
- Slow manifolds for infinite-dimensional evolution equations
- Bifurcation, perturbation of simple eigenvalues, and linearized stability
- Resolution of singularities of an algebraic variety over a field of characteristic zero. II
- Bifurcation from simple eigenvalues
- Resolution of singularities of an algebraic variety over a field of characteristic zero. I
- Infinite-dimensional dynamical systems. An introduction to dissipative parabolic PDEs and the theory of global attractors
- Extending geometric singular perturbation theory to nonhyperbolic points -- fold and canard points in two dimensions
- Extending slow manifolds near transcritical and pitchfork singularities
- À propos de canards (Apropos canards)
- Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions
- Exchange of Stabilities in Autonomous Systems
- REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS
- Existence and persistence of invariant manifolds for semiflows in Banach space
- On the Existence and Stability of Fast Traveling Waves in a Doubly Diffusive FitzHugh--Nagumo System
- Nonlinear PDEs
- Canard cycles and center manifolds
- A survey on the blow-up method for fast-slow systems
- Local Theory for Spatio-Temporal Canards and Delayed Bifurcations
- Discretized fast-slow systems near transcritical singularities
- Singularly perturbed elliptic problems in the case of exchange of stabilities
- Relaxation oscillation and canard explosion
- Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation
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