Weak stability by noise for approximations of doubly nonlinear evolution equations

2025/07/23 by Carlo Orrieri, Orrieri, Carlo, Luca Scarpa +3
Engineering · #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.17331

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.

Citations

• Pathwise uniqueness for stochastic heat and damped equations with Hölder continuous drift
• Weak uniqueness by noise for singular stochastic PDEs
• Doubly nonlinear stochastic evolution equations II
• Strong uniqueness for stochastic evolution equations with unbounded measurable drift term

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