On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs

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2021
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Dhariwal, Gaurav
Huber, Florian
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Stochastic Analysis and Applications. Taylor & Francis. 2021, 39(5), pp. 898-925. ISSN 0736-2994. eISSN 1532-9356. Available under: doi: 10.1080/07362994.2020.1857268
Zusammenfassung

The main goal of this work is to relate weak and pathwise mild solutions for parabolic quasilinear stochastic partial differential equations (SPDEs). Extending in a suitable way techniques from the theory of nonautonomous semilinear SPDEs to the quasilinear case, we prove the equivalence of these two solution concepts.

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Fachgebiet (DDC)
510 Mathematik
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Quasilinear SPDEs, cross-diffusion systems, weak solution, pathwise mild solution
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ISO 690DHARIWAL, Gaurav, Florian HUBER, Alexandra BLESSING-NEAMTU, 2021. On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs. In: Stochastic Analysis and Applications. Taylor & Francis. 2021, 39(5), pp. 898-925. ISSN 0736-2994. eISSN 1532-9356. Available under: doi: 10.1080/07362994.2020.1857268
BibTex
@article{Dhariwal2021-09-03equiv-57950,
  year={2021},
  doi={10.1080/07362994.2020.1857268},
  title={On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs},
  number={5},
  volume={39},
  issn={0736-2994},
  journal={Stochastic Analysis and Applications},
  pages={898--925},
  author={Dhariwal, Gaurav and Huber, Florian and Blessing-Neamtu, Alexandra}
}
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