On initial boundary value problems for variants of the Hunter–Saxton equation

The Hunter–Saxton equation serves as a mathematical model for orientation waves in a nematic liquid crystal. The present paper discusses a modified variant of this equation, coming up in the study of critical points for the speed of orientation waves, as well as a two-component extension. We establi...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 63; no. 3; pp. 441 - 452
Main Author Kohlmann, Martin
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.06.2012
Subjects
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
35G31
Initial boundary value problems
35B44
35B65
Hunter–Saxton equation
Well-posedness
Blow-up
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Summary:The Hunter–Saxton equation serves as a mathematical model for orientation waves in a nematic liquid crystal. The present paper discusses a modified variant of this equation, coming up in the study of critical points for the speed of orientation waves, as well as a two-component extension. We establish well-posedness and blow-up results for some initial boundary value problems for the modified Hunter–Saxton equation and the two-component Hunter–Saxton system.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-011-0154-z