Hamiltonian Formalism in Pattern Formation Problems in Dissipative Systems

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  • Kuwamura Masataka
    広島大学理学部数学科:広島大学大学院理学研究科:広島商船高等専門学校:和歌山大学システム工学部:(現)神戸大学発達科学部

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  • 散逸系のパターン形成問題に現れるハミルトン形式
  • サンイツケイ ノ パターン ケイセイ モンダイ ニ アラワレル ハミルトン ケイシキ

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It is well known that the Hamiltonian formalism plays a central role in classical mechanics. In this article, we introduce the notion of gradient/skew-gradient structure which enables us to apply the Hamiltonian formalism for studying pattern formation problems in dissipative systems. We explain usefulness of the gradient/skew-gradient structure through the linear stability analysis of standing pulse solutions and spatially periodic stationary patterns in reaction-diffusion equations, which are typical subjects of pattern formation theory in disspative systems.

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