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arXiv · 2502.11640

Generalized Yosida Approximation and Multi-Valued Stochastic Evolution Inclusions

Wujing Fan·Wei Hong·Wei Liu
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Abstract

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.

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Wujing Fan, Wei Hong, Wei Liu. 2025-07-25. Generalized Yosida Approximation and Multi-Valued Stochastic Evolution Inclusions. https://arxiv.org/abs/2502.11640

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