Rigorous numerics of finite-time singularities in dynamical systems - methodology and applications
Rigorous numerics of finite-time singularities in dynamical systems - methodology and applications
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动力系统中有限时间奇点的严格数值 - 方法和应用
DOI：
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发表时间：
2017
期刊：
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通讯作者：
Kaname Matsue
中科院分区：
文献类型：
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作者：
Kaname Matsue
本文旨在提供动力系统有限时间奇异性的严格数值计算方法。将时间尺度去广化和李雅普诺夫函数在去广化向量场不变集稳定流形上的验证与常微分方程的标准积分方法相结合，给出了包含有限时间奇点的动力系统的验证轨迹。我们的重点包括有限时间消光，带半线或紧凑支撑的行波解决方案，以及快慢系统中的奇异鸭翼，包括对消光外壳，有限通过时间或紧凑支撑尺寸的严格验证。这样的验证解导致了大量的复合波解的退化抛物方程，例如，具有具体的剖面和演化信息。结合以往工作中爆破解的严格数值，本程序还用严格数值给出了有限时间奇点的普遍方面。
This paper aims at providing rigorous numerical computation procedure for finite-time singularities in dynamical systems. Combination of time-scale desingularization as well as Lyapunov functions validation on stable manifolds of invariant sets for desingularized vector fields with standard integration procedure for ordinary differential equations give us validated trajectories of dynamical systems involving finite-time singularities. Our focus includes finite-time extinction, traveling wave solutions with half-line or compact support, and singular canards in fast-slow systems, including rigorous validations of enclosures of extinction, finite-passage times or size of supports for compactons. Such validated solutions lead to a plenty of composite wave solutions for degenerate parabolic equations, for example, with concrete information of profiles and evolutions. The present procedure also provides a universal aspect of finite-time singularities with rigorous numerics, combining with rigorous numerics of blow-up solutions in preceding works.
ODE 有限时间奇点的严格数值
DOI：
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发表时间：
2018
期刊：
影响因子：
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作者：
渡部 善隆;木下 武彦;中尾 充宏;Kaname Matsue
通讯作者：
Kaname Matsue