3 problems

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The localization conjecture for amplitude equations of non-local PDEs
The space-fractional Swift–Hohenberg equation is a non-local reaction-diffusion PDE whose critical modes arise near a bifurcation point. An amplitude equation is a reduced PDE gove…
Conjectureopenamplitude-equations nonlocal-pdes pattern-formationarXiv posted 2 days ago
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Oono–Shiwa conjecture on qualitative validity of amplitude equations
Oono–Shiwa conjecture. If a given partial differential equation is structurally stable, then its amplitude equation provides the qualitative features of the given system.
Conjectureopenamplitude-equations partial-differential-equations pattern-formationarXiv posted 2 days ago
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Amplitude-equation conjecture for stitch patterns in a moving-belt viscous thread
The thread is laid down on a moving belt, with nozzle height $H$ and belt speed $U$ as the main control parameters; the liquid has fixed flow rate $Q$ and nozzle diameter $d$ , and…
Conjectureopenamplitude-equations bifurcation-theory fluid-dynamicsarXiv posted 2 days ago

The localization conjecture for amplitude equations of non-local PDEs