期刊
NETWORKS AND HETEROGENEOUS MEDIA
卷 10, 期 2, 页码 387-399出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/nhm.2015.10.387
关键词
Chemical oscillations; pacemakers; target patterns; Kondratiev spaces; complex Ginzburg-Landau
资金
- NSF [DMS-0806614, DMS-1311740]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1311740] Funding Source: National Science Foundation
We consider localized perturbations to spatially homogeneous oscillations in dimension 3 using the complex Ginzburg-Landau equation as a prototype. In particular, we will focus on heterogeneities that locally change the phase of the oscillations. In the usual translation invariant spaces and at epsilon = 0 the linearization about these spatially homogeneous solutions result in an operator with zero eigenvalue embedded in the essential spectrum. In contrast, we show that when considered as an operator between Kondratiev spaces, the linearization is a Fredholm operator. These spaces consist of functions with algebraical localization that increases with each derivative. We use this result to construct solutions close to the equilibrium via the Implicit Function Theorem and derive asymptotics for wavenumbers in the far field.
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