Colombeau solutions to nonlinear wave equations

Details Colombeau solutions to nonlinear wave equations Colombeau solutions to nonlinear wave equations

2006-12-15

arxiv.org/abs/math/0612445v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

This paper is a tutorial that demonstrates various methods from the Colombeau theory of generalized functions in the context of semilinear wave equations. The Colombeau generalized functions constitute differential algebras that contain the space of distributions. We solve the 1D-semilinear wave equation in these algebras, show how delta waves can be computed and then turn to linear and nonlinear regularity theory.

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