A new form of asymptotic expansion for non-smooth differential equations with time-decaying forcing functions

Abstract

This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but coherent way. We prove that every decaying solution admits an asymptotic expansion of a new type. This expansion contains a new variable that allows it to be established in a closed-form, but does not affect the meaning and precision of the expansion. Moreover, the expansion is constructed explicitly with the use of the complexification method.

Differential Equations and Dynamical System, in press. The published version will have a different format

References in corpus (3)

• On the finite time blow-ups for solutions of nonlinear differential equations
• Behavior near the extinction time for systems of differential equations with sublinear dissipation terms
• Asymptotic expansions with subordinate variables for solutions of the Navier-Stokes equations