October 8, 2025Open Access

Weak stability by noise for approximations of doubly nonlinear evolution equations

Key Points

The research shows the existence of weak solutions for doubly nonlinear stochastic evolution equations, enabling stability.
Unique probabilistic characteristics arise from additive noise, affecting solution behavior and stability outcomes.
A systematic study of weak solutions in these equations illustrates their relevance in understanding stochastic systems.
The findings indicate that doubly nonlinear equations may defy traditional uniqueness expectations, revealing stochastic properties.

Abstract

Doubly nonlinear stochastic evolution equations are considered. Upon assuming the additive noise to be rough enough, we prove the existence of probabilistically weak solutions of Friedrichs type and study their uniqueness in law. This entails stability for approximations of stochastic doubly nonlinear equations in a weak probabilistic sense. Such effect is a genuinely stochastic, as doubly nonlinear equations are not even expected to exhibit uniqueness in the deterministic case.

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Cite This Study

Orrieri et al. (Wed,) studied this question.

synapsesocial.com/papers/68e6679587ecc93a24d175ac https://doi.org/https://doi.org/10.48550/arxiv.2507.17331

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