有非線性干擾的二階微分方程

Abstract

在這一篇論文中我們討論的是下列這個非線性初值問題：\n u``(t)=u`(t)^q(c_1+c_2u(t)^p)\n u(0) = u_0; u`(0) = u_1:\n我們關注於上述問題正解的一些性質。我們發現了一些爆破(Blow-up)現象，並獲得一些結果，有關爆破率(Blow-up rate)、爆破常數(Blow-up constant)以及爆破時間(Blow-up time)。

In this paper we study the following initial value problem for the nonlinear equation,\n u``(t)=u`(t)^q(c_1+c_2u(t)^p)\n u(0) = u_0; u`(0) = u_1:\nWe are interested in properties of positive solutions of the above problem.We have found blow-up phenomena and obtained some results on blowup rates, blow-up constants and life-spans.