Travelling wave solutions to some PDEs of mathematical physics
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 cos...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204108028 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |