THE STABILITY AND DYNAMICS OF HOT-SPOT SOLUTIONS TO TWO ONE-DIMENSIONAL MICROWAVE HEATING MODELS

DOI10.1142/S0219530504000291zbMath1050.35008MaRDI QIDQ4474603

David Iron, Michael J. Ward

Publication date: 12 July 2004

Published in: Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

metastabilitypinningnonlocal eigenvalue problemGierer-Meinhardt activator-inhibitor modelhot-spots

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (5)

The Existence and Stability of Spike Equilibria in the One‐Dimensional Gray–Scott Model: The Low Feed‐Rate Regime ⋮ Metastability as a coexistence mechanism in a model for dryland vegetation patterns ⋮ Existence and meta-stability of steady states of a model for chemotaxis ⋮ Spectral properties of non-local differential operators ⋮ Metastability in chemotaxis models

Uses Software

• COLSYS

Cites Work

• Large amplitude stationary solutions to a chemotaxis system
• Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model
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• The Dynamics and Pinning of a Spike for a Reaction-Diffusion System
• LAPACK Users' Guide
• Pattern formation in the one-dimensional Gray - Scott model
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• Positivity results for a nonlocal elliptic equation
• A nonlocal Sturm–Liouville eigenvalue problem
• Ginzburg--Landau Vortices: Dynamics, Pinning, and Hysteresis
• A Nonlocal Eigenvalue Problem and the Stability of Spikes for Reaction–Diffusion Systems with Fractional Reaction Rates
• On single interior spike solutions of the Gierer–Meinhardt system: uniqueness and spectrum estimates
• Homoclinic Stripe Patterns
• A Geometric Approach to Singularly Perturbed Nonlocal Reaction-Diffusion Equations
• A Metastable Spike Solution for a Nonlocal Reaction-Diffusion Model
• The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
• Spike pinning for the Gierer-Meinhardt model

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