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

[摘要] 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. (C) 2019 Published by Elsevier Inc.

[发布日期] 2019-12-05

[关键词] Blow-up solutions;Desingularization;Center manifolds;Extinction;Compacton traveling wave;Quenching