Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs

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Abstract

Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets at infinity via compactifications of phase spaces, and dynamics on their center-stable manifolds. In particular, we show that dynamics on center-stable manifolds of invariant sets at infinity with appropriate time-scale desingularizations as well as blowing-up of singularities characterize dynamics of blow-up solutions as well as their rigorous blow-up rates. Similarities for characterizing finite-time extinction and asymptotic behavior of compacton traveling waves to blow-up solutions are also shown.

Original languageEnglish
Pages (from-to)7313-7368
Number of pages56
JournalJournal of Differential Equations
Volume267
Issue number12
DOIs
Publication statusPublished - Dec 5 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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