Existence and stability of spatially localized patterns (Q1627693)
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scientific article; zbMATH DE number 6987654
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and stability of spatially localized patterns |
scientific article; zbMATH DE number 6987654 |
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Existence and stability of spatially localized patterns (English)
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3 December 2018
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The authors investigate localized structures that consist of an oscillatory pattern with finite spatial range that appears within a homogeneous background state. These structures can be viewed as gluing a front and a back together to create a localized structure. The authors provide a unified approach to rigorously address the stability of symmetric and asymmetric localized snaking solutions. It is shown that, under appropriate assumptions, temporal eigenvalues of the front and back underlying a localized solution are added with multiplicity in the right half plane. The planar Swift-Hohenberg system is used to illustrate results.
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homoclinic snaking
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planar patterns
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partial differential equations
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stability
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Evans function
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Swift-Hohenberg equation
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