Behavior near the extinction time for systems of differential equations with sublinear dissipation terms

2022/11/30 by Hoang, Luan
#34D05 #41A60 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.17241

Abstract

This paper is focused on the behavior near the extinction time of solutions of systems of ordinary differential equations with a sublinear dissipation term. Suppose the dissipation term is a product of a linear mapping A and a positively homogeneous scalar function H of a negative degree -α. Then any solution with an extinction time T_* behaves like (T_*-t)^1/αξ_* as time t→ T_*^-, where ξ_* is an eigenvector of A. The result allows the higher order terms to be general and the nonlinear function H to take very complicated forms. As a demonstration, our theoretical study is applied to an inhomogeneous population model.

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