Proof of the marginal stability bound for the Swift-Hohenberg equation and related equations

2000/05/12 by Pierre Collet, Collet, Pierre, Jean‐Pierre Eckmann +2 · 1 citation
Computer Science · Engineering · Mathematics · Medicine · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Pattern Formation and Solitons (nlin.PS) #Stability and Controllability of Differential Equations #math-ph #math.MP #nlin.PS #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.nlin/0005024

16 pages, 0 figures

arxiv created 2000/05/12 · openalex publication_date 2000/05/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if the initial condition of the Swift-Hohenberg equation ∂_t u(x,t)=(ε²-(1+∂_ x²)²) u(x,t) -u³(x,t) is bounded in modulus by Ce^-βx as x→+∞ , the solution cannot propagate to the right with a speed greater than sup_0

Citations

• Multidimensional nonlinear diffusion arising in population genetics

Cited by

• Spatio-Temporal Dynamics of Reaction-Diffusion Patterns

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