--- _id: '9307' abstract: - lang: eng text: We establish finite time extinction with probability one for weak solutions of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t12) whereas the support of solutions to the deterministic PME grows only with rate O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent shift for Wong–Zakai type approximations, the transformation to a deterministic PME with two copies of a Brownian path as the lateral boundary, and techniques from the theory of viscosity solutions. acknowledgement: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 . I am very grateful to M. Gerencsér and J. Maas for proposing this problem as well as helpful discussions. Special thanks go to F. Cornalba for suggesting the additional κ-truncation in Proposition 5. I am also indebted to an anonymous referee for pointing out a gap in a previous version of the proof of Lemma 9 (concerning the treatment of the noise term). The issue is resolved in this version. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 citation: ama: 'Hensel S. Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. 2021;9:892–939. doi:10.1007/s40072-021-00188-9' apa: 'Hensel, S. (2021). Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-021-00188-9' chicago: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium Equation with Transport Noise.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2021. https://doi.org/10.1007/s40072-021-00188-9.' ieee: 'S. Hensel, “Finite time extinction for the 1D stochastic porous medium equation with transport noise,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 9. Springer Nature, pp. 892–939, 2021.' ista: 'Hensel S. 2021. Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. 9, 892–939.' mla: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium Equation with Transport Noise.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 9, Springer Nature, 2021, pp. 892–939, doi:10.1007/s40072-021-00188-9.' short: 'S. Hensel, Stochastics and Partial Differential Equations: Analysis and Computations 9 (2021) 892–939.' date_created: 2021-04-04T22:01:21Z date_published: 2021-03-21T00:00:00Z date_updated: 2023-08-07T14:31:59Z day: '21' ddc: - '510' department: - _id: JuFi doi: 10.1007/s40072-021-00188-9 ec_funded: 1 external_id: isi: - '000631001700001' file: - access_level: open_access checksum: 6529b609c9209861720ffa4685111bc6 content_type: application/pdf creator: dernst date_created: 2021-04-06T09:31:28Z date_updated: 2021-04-06T09:31:28Z file_id: '9309' file_name: 2021_StochPartDiffEquation_Hensel.pdf file_size: 727005 relation: main_file success: 1 file_date_updated: 2021-04-06T09:31:28Z has_accepted_license: '1' intvolume: ' 9' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 892–939 project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: 'Stochastics and Partial Differential Equations: Analysis and Computations' publication_identifier: eissn: - 2194-041X issn: - 2194-0401 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Finite time extinction for the 1D stochastic porous medium equation with transport noise tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2021' ...