International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 509026, 11 pages
Research Article

Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces

Institute of Mathematics and Computer Sciences, Ural Federal University, 51 Lenina Avenue, Ekaterinburg 620083, Russia

Received 30 March 2012; Accepted 9 September 2012

Academic Editor: Palle E. Jorgensen

Copyright © 2012 Irina V. Melnikova and Uljana A. Alekseeva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Generalized solutions to the abstract Cauchy problem for a quasilinear equation with the generator of an integrated semigroup and with terms reflecting nonlinear perturbations and white noise type perturbations are under consideration. An abstract stochastic Colombeau algebra is constructed, and solutions in the algebra are studied.