论文标题
无限序列渐近膨胀，用于具有非平滑非线性的耗散微分方程的衰减溶液
Infinite series asymptotic expansions for decaying solutions of dissipative differential equations with non-smooth nonlinearity
论文作者
论文摘要
我们研究了非平凡的溶液的确切渐近行为，该溶液会收敛到零，因为时间趋向于无限，非线性普通微分方程的耗散系统。方程式的非线性项可能不具有泰勒串联的扩展。从技术上讲，这种缺失在建立渐近膨胀作为无限序列的技术上，以解决这种腐烂的解决方案。在当前的论文中，我们克服了这一限制，并随着时间的流逝而获得无限的渐近扩张。该系列的扩展为解决方案提供了较大的时间近似值，并且以任何给定的速率呈指数衰减的误差。主要思想是将非线性项的泰勒膨胀中心转移到非零点。事实证明，这一点来自解决方案的非平凡渐近行为，我们通过一种新的简单方法证明了这一点。我们的结果适用于以前尚未处理过的不同类别的非线性方程。
We study the precise asymptotic behavior of a non-trivial solution that converges to zero, as time tends to infinity, of dissipative systems of nonlinear ordinary differential equations. The nonlinear term of the equations may not possess a Taylor series expansion about the origin. This absence technically cripples previous proofs in establishing an asymptotic expansion, as an infinite series, for such a decaying solution. In the current paper, we overcome this limitation and obtain an infinite series asymptotic expansion, as time goes to infinity. This series expansion provides large time approximations for the solution with the errors decaying exponentially at any given rates. The main idea is to shift the center of the Taylor expansions for the nonlinear term to a non-zero point. Such a point turns out to come from the non-trivial asymptotic behavior of the solution, which we prove by a new and simple method. Our result applies to different classes of non-linear equations that have not been dealt with previously.
