On the convective nature of the instability of a front undergoing a supercritical Turing bifurcation

@article{Ghazaryan2009OnTC,
  title={On the convective nature of the instability of a front undergoing a supercritical Turing bifurcation},
  author={Anna Ghazaryan},
  journal={Math. Comput. Simul.},
  year={2009},
  volume={80},
  pages={10-19}
}
  • A. Ghazaryan
  • Published 1 September 2009
  • Physics
  • Math. Comput. Simul.
1 Citations

Figures from this paper

Stability of Gasless Combustion Fronts in One-Dimensional Solids
For gasless combustion in a one-dimensional solid, we show a type of nonlinear stability of the physical combustion front: if a perturbation of the front is small in both a spatially uniform norm and

References

SHOWING 1-10 OF 15 REFERENCES
Essential instabilities of fronts: bifurcation, and bifurcation failure
Various instability mechanisms of fronts in reaction-diffusion systems are analysed; the emphasis is on instabilities that have the potential to create modulated (i.e. time-periodic) waves near the
Instabilities and fronts in extended systems
The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations,
Stable transport of information near essentially unstable localized structures
When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This
Non-linear Stability of Modulated Fronts¶for the Swift–Hohenberg Equation
Abstract: We consider front solutions of the Swift–Hohenberg equation ∂tu= -(1+ ∂x2)2u + ɛ2u -u3. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using
Attractors for modulation equations on unbounded domains-existence and comparison
We are interested in the long-time behaviour of nonlinear parabolic PDEs defined on unbounded cylindrical domains. For dissipative systems defined on bounded domains, the longtime behaviour can often
Hopf Bifurcation and Exchange of Stability in Diffusive Media
Abstract.We consider solutions bifurcating from a spatially homogeneous equilibrium under the assumption that the associated linearization possesses a continuous spectrum up to the imaginary axis,
Nonlinear Convective Instability of Turing-Unstable Fronts near Onset: A Case Study
TLDR
Fronts are traveling waves in spatially extended systems that connect two different spatially homogeneous rest states and if the rest state behind the front undergoes a supercritical Turing instabilitator, the front becomes supercritical itself.
Asymptotic stability of solitary waves
AbstractWe show that the family of solitary waves (1-solitons) of the Korteweg-de Vries equation $$\partial _t u + u\partial _x u + \partial _x^3 u = 0 ,$$ is asymptotically stable. Our methods also
Local stability of critical fronts in nonlinear parabolic partial differential equations
For the Ginzburg-Landau equation and similar nonlinear parabolic partial differential equations on the real line, we prove the nonlinear stability of the slowest monotonic front solution by computing
...
...