Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise
We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem raised in [Barbu, R\"ockner; JDE, 2011], [Barbu, R\"o...
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| Format: | Journal article |
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2018
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| _version_ | 1797090208670285824 |
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| author | Fehrman, B Gess, B |
| author_facet | Fehrman, B Gess, B |
| author_sort | Fehrman, B |
| collection | OXFORD |
| description | We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem raised in [Barbu, R\"ockner; JDE, 2011], [Barbu, R\"ockner; JDE, 2018+], and [Gess, AoP, 2014]. |
| first_indexed | 2024-03-07T03:15:12Z |
| format | Journal article |
| id | oxford-uuid:b58ea192-e52c-40e3-b6ea-6213add7deb0 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:15:12Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | oxford-uuid:b58ea192-e52c-40e3-b6ea-6213add7deb02022-03-27T04:34:19ZPath-by-path well-posedness of nonlinear diffusion equations with multiplicative noiseJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b58ea192-e52c-40e3-b6ea-6213add7deb0Symplectic Elements at Oxford2018Fehrman, BGess, BWe prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem raised in [Barbu, R\"ockner; JDE, 2011], [Barbu, R\"ockner; JDE, 2018+], and [Gess, AoP, 2014]. |
| spellingShingle | Fehrman, B Gess, B Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise |
| title | Path-by-path well-posedness of nonlinear diffusion equations with
multiplicative noise |
| title_full | Path-by-path well-posedness of nonlinear diffusion equations with
multiplicative noise |
| title_fullStr | Path-by-path well-posedness of nonlinear diffusion equations with
multiplicative noise |
| title_full_unstemmed | Path-by-path well-posedness of nonlinear diffusion equations with
multiplicative noise |
| title_short | Path-by-path well-posedness of nonlinear diffusion equations with
multiplicative noise |
| title_sort | path by path well posedness of nonlinear diffusion equations with multiplicative noise |
| work_keys_str_mv | AT fehrmanb pathbypathwellposednessofnonlineardiffusionequationswithmultiplicativenoise AT gessb pathbypathwellposednessofnonlineardiffusionequationswithmultiplicativenoise |