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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.11640 |
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| _version_ | 1866915408734322688 |
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| author | Fan, Wujing Hong, Wei Liu, Wei |
| author_facet | Fan, Wujing Hong, Wei Liu, Wei |
| contents | In this paper, we generalize the classical Yosida approximation by utilizing a nonstandard duality mapping to establish the existence and uniqueness of both (probabilistically) weak and strong solutions and demonstrate the continuous dependence on initial values for a class of multi-valued stochastic evolution inclusions within the variational framework.
Furthermore, leveraging this generalized Yosida approximation, we derive the finite-time extinction of solutions with probability one and also provide an explicit upper bound of the moment of extinction time for multi-valued stochastic evolution inclusions perturbed by linear multiplicative noise. The main results are applicable to various examples, including multi-valued stochastic porous media equations, stochastic $Φ$-Laplace equations and stochastic evolution inclusions involving subdifferentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Yosida Approximation and Multi-Valued Stochastic Evolution Inclusions Fan, Wujing Hong, Wei Liu, Wei Probability In this paper, we generalize the classical Yosida approximation by utilizing a nonstandard duality mapping to establish the existence and uniqueness of both (probabilistically) weak and strong solutions and demonstrate the continuous dependence on initial values for a class of multi-valued stochastic evolution inclusions within the variational framework. Furthermore, leveraging this generalized Yosida approximation, we derive the finite-time extinction of solutions with probability one and also provide an explicit upper bound of the moment of extinction time for multi-valued stochastic evolution inclusions perturbed by linear multiplicative noise. The main results are applicable to various examples, including multi-valued stochastic porous media equations, stochastic $Φ$-Laplace equations and stochastic evolution inclusions involving subdifferentials. |
| title | Generalized Yosida Approximation and Multi-Valued Stochastic Evolution Inclusions |
| topic | Probability |
| url | https://arxiv.org/abs/2502.11640 |