Non-constant stable solutions to Landau-Lifshitz equation (Q1265708)
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scientific article; zbMATH DE number 1202527
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-constant stable solutions to Landau-Lifshitz equation |
scientific article; zbMATH DE number 1202527 |
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Non-constant stable solutions to Landau-Lifshitz equation (English)
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17 March 1999
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The author proves the existence of solutions to the static Landau-Lifshitz equation corresponding to the homotopy classes of continuous functions from \(\Omega \rightarrow S^2 \cap \{u_3 = 0\}\). Here \(\Omega\) is a non-simply connected bounded domain in \(\mathbb{R}^3\). The stability of the solutions to the time-dependent Landau-Lifshitz equation is also obtained. Moreover, it is proved a result about the non-existence of non-constant solutions to the static Landau-Lifshitz equation.
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static Landau-Lifshitz equation
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homotopy classes
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Schauder's fixed point theorem
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non-existence
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