Freezing Solutions of Equivariant Evolution Equations

DOI10.1137/030600515zbMath1061.65078OpenAlexW2005761796MaRDI QIDQ4653116

V. Thümmler, Wolf-Jürgen Beyn

Publication date: 28 February 2005

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/451bef9359403591d10b97692544b23876ec270d

zbMATH Keywords

Lie groupsreaction-diffusion systemsunbounded domainsBanach spaceequivariancetraveling wave solutionpartial differential algebraic equationsasymptotic boundary conditionsfinite differences in spacegeneral evolution equationsspiral solutionsfrozen solutionhalf-explicit Euler methods in time

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Reaction-diffusion equations (35K57) Nonlinear differential equations in abstract spaces (34G20) Partial functional-differential equations (35R10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (45)

Stability of Traveling Oscillating Fronts in Complex Ginzburg Landau Equations ⋮ Manifold Approximations via Transported Subspaces: Model Reduction for Transport-Dominated Problems ⋮ Reduced basis methods for time-dependent problems ⋮ Stability of concatenated traveling waves ⋮ Spectral analysis of localized rotating waves in parabolic systems ⋮ EQUATION-FREE, EFFECTIVE COMPUTATION FOR DISCRETE SYSTEMS: A TIME STEPPER BASED APPROACH ⋮ Model Order Reduction for Stochastic Dynamical Systems with Continuous Symmetries ⋮ Computation and Stability of Traveling Waves in Second Order Evolution Equations ⋮ Cartography of high-dimensional flows: A visual guide to sections and slices ⋮ Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing ⋮ Comparison of diagonal-implicit, linear-implicit and half-explicit Runge-Kutta methods in nonlinear finite element analyses ⋮ Exact coherent structures and chaotic dynamics in a model of cardiac tissue ⋮ Periodic orbit analysis of a system with continuous symmetry—A tutorial ⋮ Pushed-to-pulled front transitions: continuation, speed scalings, and hidden monotonicty ⋮ Continuous symmetry reduction and return maps for high-dimensional flows ⋮ Phase Reduction of Waves, Patterns, and Oscillations Subject to Spatially Extended Noise ⋮ Freezing similarity solutions in the multi-dimensional Burgers equation ⋮ Reduction of continuous symmetries of chaotic flows by the method of slices ⋮ Two-dimensional traveling waves arising from planar front interaction in a three-species competition-diffusion system ⋮ Stability and freezing of nonlinear waves in first order hyperbolic PDEs ⋮ On a nonlocal moving frame approximation of traveling waves ⋮ Numerical bifurcation theory for high-dimensional neural models ⋮ The effect of freezing and discretization to the asymptotic stability of relative equilibria ⋮ Fronts and bumps in spatially extended Kuramoto networks ⋮ A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME ⋮ Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations ⋮ The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena ⋮ Instability in large bounded domains—branched versus unbranched resonances ⋮ Revealing the state space of turbulent pipe flow by symmetry reduction ⋮ A Huygens principle for diffusion and anomalous diffusion in spatially extended systems ⋮ Linear stability of traveling waves in first-order hyperbolic PDEs ⋮ Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system ⋮ Projective and coarse projective integration for problems with continuous symmetries ⋮ Metastability of solitary waves in diatomic FPUT lattices ⋮ Model Order Reduction for Problems with Large Convection Effects ⋮ Stability of Traveling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations ⋮ Dynamics of Patterns in Nonlinear Equivariant PDEs ⋮ PDE Methods for Two-Dimensional Neural Fields ⋮ Computation and stability of waves in equivariant evolution equations ⋮ Projection-based model reduction with dynamically transformed modes ⋮ Optimization-Based Modal Decomposition for Systems with Multiple Transports ⋮ A learning-based projection method for model order reduction of transport problems ⋮ Modal decomposition of flow data via gradient-based transport optimization ⋮ Domain Wall Motion in Axially Symmetric Spintronic Nanowires ⋮ Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems

This page was built for publication: Freezing Solutions of Equivariant Evolution Equations