Modulating traveling fronts in a dispersive Swift-Hohenberg equation coupled to an additional conservation law

Hilder, Bastian

doi:10.1016/j.jmaa.2022.126224

Journal of Mathematical Analysis and Applications

2022

DOI: 10.1016/j.jmaa.2022.126224

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Modulating traveling fronts in a dispersive Swift-Hohenberg equation coupled to an additional conservation law

Bastian Hilder

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2024

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Global Existence for Long Wave Hopf Unstable Spatially Extended Systems with a Conservation Law

Gauss,

Logioti,

Schneider

et al. 2024

J Dyn Diff Equat

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We are interested in reaction–diffusion systems, with a conservation law, exhibiting a Hopf bifurcation at the spatial wave number $$ k = 0 $$ k = 0 . With the help of a multiple scaling perturbation ansatz a Ginzburg–Landau equation coupled to a scalar conservation law can be derived as an amplitude system for the approximate description of the dynamics of the original reaction–diffusion system near the first instability. We use the amplitude system to show the global existence of all solutions starting in a small neighborhood of the weakly unstable ground state for original systems posed on a large spatial interval with periodic boundary conditions.

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Global Existence for Long Wave Hopf Unstable Spatially Extended Systems with a Conservation Law

Gauss,

Logioti,

Schneider

et al. 2024

J Dyn Diff Equat

View full text Add to dashboard Cite

show abstract

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Modulating traveling fronts in a dispersive Swift-Hohenberg equation coupled to an additional conservation law

Cited by 1 publication

References 29 publications

Global Existence for Long Wave Hopf Unstable Spatially Extended Systems with a Conservation Law

Global Existence for Long Wave Hopf Unstable Spatially Extended Systems with a Conservation Law

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