期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S0161171204108028
出版社：Hindawi Publishing Corporation
摘要：Nonlinear operations such as multiplication of distributions are
not allowed in the classical theory of distributions. As a result,
some ambiguities arise when we want to solve nonlinear partial
differential equations such as differential equations of
elasticity and multifluid flows, or some new cosmological models
such as signature changing space-times. Colombeau's new theory of
generalized functions can be used to remove these ambiguities. In
this paper, we first consider a simplified model of elasticity and
multifluid flows in the framework of Colombeau's theory and show
how one can handle such problems, investigate their jump conditions, and resolve their ambiguities. Then we consider as a
new proposal the case of cosmological models with signature
change and use Colombeau's theory to solve Einstein equation for
the beginning of the Universe.
