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Doubly nonlinear stochastic evolution equations II

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Abstract

Completing the analysis in Scarpa (Math Models Methods Appl Sci 30(5): 991–1031 2020), we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modeling of dissipative media and correspond to generalized balance laws between conservative and nonconservative dynamics. We extend the reach of the classical deterministic case by allowing for stochasticity. The existence of martingale solutions is proved via a regularization technique, hinging on the validity of an Itô formula in a minimal regularity setting. Under additional assumptions, the well-posedness of stochastically strong solutions is also shown.

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Acknowledgements

LS was funded by the Austrian Science Fund (FWF) through the Lise-Meitner project M 2876. US is partially supported by the Austrian Science Fund (FWF) through projects F 65, I 4354, P 32788, W 1245, I 5149 and by the OeAD-WTZ project CZ 01/2021.

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Authors and Affiliations

  1. Department of Mathematics, Politecnico di Milano, via E. Bonaldi 9, 20133, Milano, Italy

    Luca Scarpa

  2. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Ulisse Stefanelli

  3. Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Str. 17, 1090, Vienna, Austria

    Ulisse Stefanelli

  4. Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes - CNR, v. Ferrata 1, 27100, Pavia, Italy

    Ulisse Stefanelli

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  1. Luca Scarpa
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  2. Ulisse Stefanelli
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Correspondence to Ulisse Stefanelli.

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Scarpa, L., Stefanelli, U. Doubly nonlinear stochastic evolution equations II. Stoch PDE: Anal Comp 11, 307–347 (2023). https://doi.org/10.1007/s40072-021-00229-3

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