Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces
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 sol...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/509026 |
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| _version_ | 1832556182104965120 |
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| author | Irina V. Melnikova Uljana A. Alekseeva |
| author_facet | Irina V. Melnikova Uljana A. Alekseeva |
| author_sort | Irina V. Melnikova |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-50bc35154c8b46f3b4d9756abd0af927 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-50bc35154c8b46f3b4d9756abd0af9272025-02-03T05:46:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/509026509026Quasilinear Stochastic Cauchy Problem in Abstract Colombeau SpacesIrina V. Melnikova0Uljana A. Alekseeva1Institute of Mathematics and Computer Sciences, Ural Federal University, 51 Lenina Avenue, Ekaterinburg 620083, RussiaInstitute of Mathematics and Computer Sciences, Ural Federal University, 51 Lenina Avenue, Ekaterinburg 620083, RussiaGeneralized 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.http://dx.doi.org/10.1155/2012/509026 |
| spellingShingle | Irina V. Melnikova Uljana A. Alekseeva Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces |
| title_full | Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces |
| title_fullStr | Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces |
| title_full_unstemmed | Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces |
| title_short | Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces |
| title_sort | quasilinear stochastic cauchy problem in abstract colombeau spaces |
| url | http://dx.doi.org/10.1155/2012/509026 |
| work_keys_str_mv | AT irinavmelnikova quasilinearstochasticcauchyprobleminabstractcolombeauspaces AT uljanaaalekseeva quasilinearstochasticcauchyprobleminabstractcolombeauspaces |