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Probabilistic Weak Solutions for Nonlinear Stochastic Evolution Problems Involving Pseudomonotone Operators

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. University of Pretoria, Pretoria, South Africa

    Z. I. Ali & M. Sango

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  1. Z. I. Ali
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  2. M. Sango
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Correspondence to M. Sango.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 7, pp. 871–892, July, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i7.2286.

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Ali, Z.I., Sango, M. Probabilistic Weak Solutions for Nonlinear Stochastic Evolution Problems Involving Pseudomonotone Operators. Ukr Math J 74, 997–1020 (2022). https://doi.org/10.1007/s11253-022-02117-y

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