Blow up of solutions to second sound equation in one space dimension,

• KATO Keiichi

  Department of Mathematics Tokyo University of Science

• SUGIYAMA Yuusuke

  Department of Mathematics Tokyo University of Science

書誌事項

タイトル別名

• BLOW UP OF SOLUTIONS TO THE SECOND SOUND EQUATION IN ONE SPACE DIMENSION

抄録

In this paper, we study blow ups of solutions to the second sound equation ∂_t²u=u∂_x(u∂_xu), which is more natural than the second sound equation in Landau-Lifshitz's text in large time. We assume that the initial data satisfies u(0,x)≥ δ>0 for some δ. We give sufficient conditions that two types of blow up occur: one of the two types is that L^∞-norm of ∂_tu or ∂_xu goes up to the infinity; the other type is that u vanishes, that is, the equation degenerates.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 67 (1), 129-142, 2013

  九州大学大学院数理学研究院

キーワード

• blow up
• quasilinear hyperbolic

詳細情報

• CRID: 1390282680204492160
• NII論文ID: 130003364804
• DOI: 10.2206/kyushujm.67.129
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/67/1/67_129/_pdf
• 本文言語コード: en
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