广义函数作为数学和物理中非光滑非线性问题的工具
Generalized functions as a tool for nonsmooth nonlinear problems in mathematics and physics
摘要：
提出了一种非线性广义函数的微分代数，作为研究非光滑非线性问题的工具。微分代数的力量被用来做数学计算或证明;那么最终的结果往往是一个经典函数或分布，而不是经典或分布意义上的解。本文的目的是邀请读者在应用这个工具在自己的研究中没有显着的先决条件，通过介绍它的使用从数学和物理的基本应用程序的样本。本文是2007年1月在新奥尔良举行的AMS 2007年年会上的一次谈话的书面版本。
英文摘要：
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final result is often a classical function or distribution which is not solution in the classical or distributional sense. The aim of this text is to invite the readers in applying this tool in their own research without significant prerequisites by presenting its use on a sample of elementary applications from mathematics and physics. This text is the written version of a talk at the 2007 annual meeting of the AMS, NewOrleans, january 2007.
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