Infinite-dimensional Evans function theory for elliptic eigenvalue problems in a channel

DOI10.1016/j.jde.2005.09.007zbMath1115.35091OpenAlexW2004658667MaRDI QIDQ2496723

Jian Deng, Shunsaku Nii

Publication date: 20 July 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2005.09.007

zbMATH Keywords

Evans functiontravelling wavedeterminant bundleFredholm Grassmannian

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05)

Related Items

Evans functions for periodic waves on infinite cylindrical domains ⋮ Edge states for second order elliptic operators in a channel ⋮ Unstable Stokes waves ⋮ Morse-Smale index theorems for elliptic boundary deformation problems ⋮ A dynamical approach to semilinear elliptic equations ⋮ Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves ⋮ Evans functions, Jost functions, and Fredholm determinants ⋮ An infinite-dimensional Evans function theory for elliptic boundary value problems ⋮ Grassmannian spectral shooting ⋮ Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems ⋮ The Morse and Maslov indices for multidimensional Schrödinger operators with matrix-valued potentials ⋮ The infinite dimensional Evans function

Cites Work

• Stability of semi-discrete shock profiles by means of an Evans function in infinite dimensions
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• Existence and stability of asymptotically oscillatory triple pulses
• A strong unique continuation theorem for parabolic equations
• Finite-wavelength stability of capillary-gravity solitary waves
• Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
• Wave-solutions of reversible systems and applications
• Evans function and blow-up methods in critical eigenvalue problems
• The homotopy type of the unitary group of Hilbert space
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• On the Structure of Spectra of Modulated Travelling Waves
• An Extension of the Stability Index for Traveling-Wave Solutions and Its Application to Bifurcations
• Defects in Oscillatory Media: Toward a Classification
• Viscous and inviscid stability of multidimensional planar shock fronts
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