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- Title
Probabilistic Weak Solutions for Nonlinear Stochastic Evolution Problems Involving Pseudomonotone Operators.
- Authors
Ali, Z. I.; Sango, M.
- Abstract
We study an important class of stochastic nonlinear evolution problems with pseudomonotone elliptic parts and establish the existence of probabilistic weak (or martingale) solutions. No solvability theory has been developed so far for these equations despite numerous works involving various generalizations of the monotonicity condition. Key to our work is a sign result for the Itô differential of an approximate solution that we establish, as well as several compactness results of the analytic and probabilistic nature, and a characterization of pseudomonotone operators due to F. E. Browder.
- Subjects
STIMULUS generalization; NONLINEAR equations; MARTINGALES (Mathematics); PSEUDODIFFERENTIAL operators; EQUATIONS
- Publication
Ukrainian Mathematical Journal, 2022, Vol 74, Issue 7, p997
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-022-02117-y