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Regularization and Well-Posedness by Noise for Ordinary and Partial Differential Equations

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Stochastic Partial Differential Equations and Related Fields (SPDERF 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 229))

Abstract

We give a brief introduction and overview of the topic of regularization and well-posedness by noise for ordinary and partial differential equations. The article is an attempt to outline in a concise fashion different directions of research in this field that have attracted attention in recent years. We close the article with a look on more recent developments in the field of nonlinear SPDE, focusing on stochastic scalar conservation laws and porous media equations. The article is tailored at master/PhD level, trying to allow a smooth introduction to the subject and pointing at a large list of references to allow further in-depth study.

Dedicated to Michael Röckner in honor of his 60th birthday.

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  1. Max-Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany

    Benjamin Gess

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Editors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Bonn, Germany

    Andreas Eberle

  2. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Martin Grothaus

  3. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Walter Hoh

  4. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Moritz Kassmann

  5. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Wilhelm Stannat

  6. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, Korea (Republic of)

    Gerald Trutnau

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Gess, B. (2018). Regularization and Well-Posedness by Noise for Ordinary and Partial Differential Equations. In: Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-319-74929-7_3

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