Perturbation of the spectra for asymptotically constant differential operators and applications

DOI10.1016/j.physd.2023.133735zbMath1514.35031arXiv2210.04748OpenAlexW4360943652MaRDI QIDQ6102480

Shuang Chen, Jin-qiao Duan

Publication date: 8 May 2023

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.04748

zbMATH Keywords

stabilityperturbation theorybifurcationGinzburg-Landau equationFitzHugh-Nagumo systemhyperbolic Burgers-Fisher model

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) General spectral theory of ordinary differential operators (34L05) Bifurcations in context of PDEs (35B32) Methods of ordinary differential equations applied to PDEs (35A24)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The modulational instability for a generalized Korteweg-de Vries equation
• Hyperbolic conservation laws with relaxation
• Geometric theory of semilinear parabolic equations
• Dichotomies in stability theory
• Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves
• Perturbation theory for linear operators.
• Exponential dichotomies and transversal homoclinic points
• Existence of traveling wave solutions in a diffusive predator-prey model
• On the structure of the spectra of periodic travelling waves
• Spectral and dynamical stability of nonlinear waves
• Fixed point theory and nonlinear problems
• Rigorous Justification of the Whitham Modulation Equations for the Generalized Korteweg-de Vries Equation
• Traveling Waves in Diffusive Predator–Prey Equations: Periodic Orbits and Point-to-Periodic Heteroclinic Orbits
• Exponential Dichotomies and Fredholm Operators
• Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation
• Instability of quasiperiodic solutions of the Ginzburg–Landau equation
• Traveling Waves in a Simplified Model of Calcium Dynamics
• Existence and spectral instability of bounded spatially periodic traveling waves for scalar viscous balance laws
• Direct Characterization of Spectral Stability of Small-Amplitude Periodic Waves in Scalar Hamiltonian Problems via Dispersion Relation
• Heat waves
• Finite bandwidth, finite amplitude convection
• Instability of small-amplitude periodic waves from fold-Hopf bifurcation
• Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source