散逸系のパターン形成問題に現れるハミルトン形式
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概要
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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.
- 一般社団法人日本応用数理学会の論文
- 2006-03-28