Stochastic Quasilinear Evolution Equations in UMD Banach Spaces
In this work we prove the existence and uniqueness up to a stopping time for the stochastic counterpart of Tosio Kato's quasilinear evolutions in UMD Banach spaces. These class of evolutions are known to cover a large class of physically important nonlinear partial differential equations. Exist...
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AFIT Scholar
2017
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| Online Erişim: | https://scholar.afit.edu/facpub/462 https://onlinelibrary.wiley.com/doi/am-pdf/10.1002/mana.201600015 |
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| _version_ | 1870453234866323456 |
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| author | Mohan, Manil T. Sritharan, Sivaguru S. |
| author_facet | Mohan, Manil T. Sritharan, Sivaguru S. |
| author_sort | Mohan, Manil T. |
| building | US Air Force Institute of Technology (AFIT) |
| collection | AFIT Scholar |
| description | In this work we prove the existence and uniqueness up to a stopping time for the stochastic counterpart of Tosio Kato's quasilinear evolutions in UMD Banach spaces. These class of evolutions are known to cover a large class of physically important nonlinear partial differential equations. Existence of a unique maximal solution as well as an estimate on the probability of positivity of stopping time is obtained. An example of stochastic Euler and Navier–Stokes equation is also given as an application of abstract theory to concrete models. |
| format | text |
| id | afit-facpub-1471 |
| institution | US Air Force Institute of Technology |
| publishDate | 2017 |
| publisher | AFIT Scholar |
| record_format | dspace |
| spelling | afit-facpub-1471 Stochastic Quasilinear Evolution Equations in UMD Banach Spaces Mohan, Manil T. Sritharan, Sivaguru S. In this work we prove the existence and uniqueness up to a stopping time for the stochastic counterpart of Tosio Kato's quasilinear evolutions in UMD Banach spaces. These class of evolutions are known to cover a large class of physically important nonlinear partial differential equations. Existence of a unique maximal solution as well as an estimate on the probability of positivity of stopping time is obtained. An example of stochastic Euler and Navier–Stokes equation is also given as an application of abstract theory to concrete models. 2017-09-01T07:00:00Z text application/pdf https://scholar.afit.edu/facpub/462 info:doi/<a href="https://doi.org/10.1002/mana.201600015">10.1002/mana.201600015</a> https://onlinelibrary.wiley.com/doi/am-pdf/10.1002/mana.201600015 Faculty Publications AFIT Scholar 35R60 Partial Differential Equations |
| spellingShingle | 35R60 Partial Differential Equations Mohan, Manil T. Sritharan, Sivaguru S. Stochastic Quasilinear Evolution Equations in UMD Banach Spaces |
| title | Stochastic Quasilinear Evolution Equations in UMD Banach Spaces |
| title_full | Stochastic Quasilinear Evolution Equations in UMD Banach Spaces |
| title_fullStr | Stochastic Quasilinear Evolution Equations in UMD Banach Spaces |
| title_full_unstemmed | Stochastic Quasilinear Evolution Equations in UMD Banach Spaces |
| title_short | Stochastic Quasilinear Evolution Equations in UMD Banach Spaces |
| title_sort | stochastic quasilinear evolution equations in umd banach spaces |
| topic | 35R60 Partial Differential Equations |
| url | https://scholar.afit.edu/facpub/462 https://onlinelibrary.wiley.com/doi/am-pdf/10.1002/mana.201600015 |
| work_keys_str_mv | AT mohanmanilt stochasticquasilinearevolutionequationsinumdbanachspaces AT sritharansivagurus stochasticquasilinearevolutionequationsinumdbanachspaces |