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Acta Acustica. 2025;9(65). doi:10.1051/aacus/2025044"},"intvolume":" 9","year":"2025","user_id":"11829","department":[{"_id":"49"}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"62000","language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","publication":"Acta Acustica","status":"public"},{"external_id":{"arxiv":["2411.14900"]},"language":[{"iso":"eng"}],"publication":"Mathematical Models and Methods in Applied Sciences","publisher":"World Scientific Pub Co Pte Ltd","date_created":"2024-06-20T13:43:42Z","title":"A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions","issue":"11","year":"2025","project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"54837","user_id":"11829","department":[{"_id":"90"},{"_id":"49"}],"type":"journal_article","status":"public","date_updated":"2026-01-05T07:59:41Z","oa":"1","author":[{"first_name":"Leander","id":"11829","full_name":"Claes, Leander","orcid":"0000-0002-4393-268X","last_name":"Claes"},{"first_name":"Johannes","full_name":"Lankeit, Johannes","last_name":"Lankeit"},{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"volume":35,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2411.14900"}],"doi":"10.1142/s0218202525500447","publication_identifier":{"issn":["1793-6314"]},"citation":{"mla":"Claes, Leander, et al. “A Model for Heat Generation by Acoustic Waves in Piezoelectric Materials: Global Large-Data Solutions.” Mathematical Models and Methods in Applied Sciences, vol. 35, no. 11, World Scientific Pub Co Pte Ltd, 2025, pp. 2465–512, doi:10.1142/s0218202525500447.","bibtex":"@article{Claes_Lankeit_Winkler_2025, title={A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions}, volume={35}, DOI={10.1142/s0218202525500447}, number={11}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Claes, Leander and Lankeit, Johannes and Winkler, Michael}, year={2025}, pages={2465–2512} }","short":"L. Claes, J. Lankeit, M. Winkler, Mathematical Models and Methods in Applied Sciences 35 (2025) 2465–2512.","apa":"Claes, L., Lankeit, J., & Winkler, M. (2025). A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions. Mathematical Models and Methods in Applied Sciences, 35(11), 2465–2512. https://doi.org/10.1142/s0218202525500447","ama":"Claes L, Lankeit J, Winkler M. A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions. Mathematical Models and Methods in Applied Sciences. 2025;35(11):2465-2512. doi:10.1142/s0218202525500447","ieee":"L. Claes, J. Lankeit, and M. Winkler, “A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions,” Mathematical Models and Methods in Applied Sciences, vol. 35, no. 11, pp. 2465–2512, 2025, doi: 10.1142/s0218202525500447.","chicago":"Claes, Leander, Johannes Lankeit, and Michael Winkler. “A Model for Heat Generation by Acoustic Waves in Piezoelectric Materials: Global Large-Data Solutions.” Mathematical Models and Methods in Applied Sciences 35, no. 11 (2025): 2465–2512. https://doi.org/10.1142/s0218202525500447."},"intvolume":" 35","page":"2465-2512"},{"status":"public","publication":"2025 International Congress on Ultrasonics","type":"conference","language":[{"iso":"eng"}],"_id":"62299","project":[{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"department":[{"_id":"49"},{"_id":"151"}],"user_id":"11829","year":"2025","place":"Paderborn","page":"138–141","citation":{"chicago":"Friesen, Olga, Claus Scheidemann, Leander Claes, Tobias Hemsel, and Bernd Henning. “Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed Langevin Transducer.” In 2025 International Congress on Ultrasonics, 138–141. 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Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed Langevin Transducer. 2025 International Congress on Ultrasonics, 138–141. https://doi.org/10.5162/ultrasonic2025/a18-a4","bibtex":"@inproceedings{Friesen_Scheidemann_Claes_Hemsel_Henning_2025, place={Paderborn}, title={Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed Langevin Transducer}, DOI={10.5162/ultrasonic2025/a18-a4}, booktitle={2025 International Congress on Ultrasonics}, publisher={AMA Service GmbH}, author={Friesen, Olga and Scheidemann, Claus and Claes, Leander and Hemsel, Tobias and Henning, Bernd}, year={2025}, pages={138–141} }","short":"O. Friesen, C. Scheidemann, L. Claes, T. Hemsel, B. Henning, in: 2025 International Congress on Ultrasonics, AMA Service GmbH, Paderborn, 2025, pp. 138–141.","mla":"Friesen, Olga, et al. “Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed Langevin Transducer.” 2025 International Congress on Ultrasonics, AMA Service GmbH, 2025, pp. 138–141, doi:10.5162/ultrasonic2025/a18-a4."},"title":"Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed Langevin Transducer","doi":"10.5162/ultrasonic2025/a18-a4","date_updated":"2026-01-05T08:00:48Z","publisher":"AMA Service GmbH","date_created":"2025-11-25T12:23:06Z","author":[{"last_name":"Friesen","id":"44026","full_name":"Friesen, Olga","first_name":"Olga"},{"first_name":"Claus","last_name":"Scheidemann","id":"38259","full_name":"Scheidemann, Claus"},{"first_name":"Leander","orcid":"0000-0002-4393-268X","last_name":"Claes","full_name":"Claes, Leander","id":"11829"},{"first_name":"Tobias","full_name":"Hemsel, Tobias","id":"210","last_name":"Hemsel"},{"first_name":"Bernd","full_name":"Henning, Bernd","id":"213","last_name":"Henning"}]},{"project":[{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"_id":"62298","user_id":"11829","department":[{"_id":"49"}],"language":[{"iso":"eng"}],"type":"conference","publication":"2025 International Congress on Ultrasonics","status":"public","date_updated":"2026-01-05T08:01:47Z","publisher":"AMA Service GmbH","date_created":"2025-11-25T12:23:06Z","author":[{"full_name":"Kuess, Raphael","last_name":"Kuess","first_name":"Raphael"},{"first_name":"Olga","last_name":"Friesen","id":"44026","full_name":"Friesen, Olga"},{"full_name":"Henning, Bernd","id":"213","last_name":"Henning","first_name":"Bernd"},{"first_name":"Andrea","full_name":"Walther, Andrea","last_name":"Walther"}],"title":"Identification of temperature-dependent material parameter functions in piezoelectricity","doi":"10.5162/ultrasonic2025/a18-a3","place":"Germany","year":"2025","citation":{"chicago":"Kuess, Raphael, Olga Friesen, Bernd Henning, and Andrea Walther. “Identification of Temperature-Dependent Material Parameter Functions in Piezoelectricity.” In 2025 International Congress on Ultrasonics, 134–137. 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Identification of temperature-dependent material parameter functions in piezoelectricity. 2025 International Congress on Ultrasonics, 134–137. https://doi.org/10.5162/ultrasonic2025/a18-a3","mla":"Kuess, Raphael, et al. “Identification of Temperature-Dependent Material Parameter Functions in Piezoelectricity.” 2025 International Congress on Ultrasonics, AMA Service GmbH, 2025, pp. 134–137, doi:10.5162/ultrasonic2025/a18-a3.","bibtex":"@inproceedings{Kuess_Friesen_Henning_Walther_2025, place={Germany}, title={Identification of temperature-dependent material parameter functions in piezoelectricity}, DOI={10.5162/ultrasonic2025/a18-a3}, booktitle={2025 International Congress on Ultrasonics}, publisher={AMA Service GmbH}, author={Kuess, Raphael and Friesen, Olga and Henning, Bernd and Walther, Andrea}, year={2025}, pages={134–137} }","short":"R. Kuess, O. Friesen, B. Henning, A. Walther, in: 2025 International Congress on Ultrasonics, AMA Service GmbH, Germany, 2025, pp. 134–137."},"page":"134–137"},{"year":"2025","citation":{"chicago":"Friesen, Olga, Lars Meihost, Kevin Koch, Leander Claes, and Bernd Henning. “Estimation of Piezoelectric Material Parameters under Varying Electric Field Conditions,” 2025. https://doi.org/10.71568/DASDAGA2025.078.","ieee":"O. Friesen, L. Meihost, K. Koch, L. Claes, and B. Henning, “Estimation of piezoelectric material parameters under varying electric field conditions,” presented at the DAS | DAGA 2025 - 51st Annual Meeting on Acoustics, Copenhagen, 2025, doi: 10.71568/DASDAGA2025.078.","ama":"Friesen O, Meihost L, Koch K, Claes L, Henning B. Estimation of piezoelectric material parameters under varying electric field conditions. In: ; 2025. doi:10.71568/DASDAGA2025.078","apa":"Friesen, O., Meihost, L., Koch, K., Claes, L., & Henning, B. (2025). Estimation of piezoelectric material parameters under varying electric field conditions. DAS | DAGA 2025 - 51st Annual Meeting on Acoustics, Copenhagen. https://doi.org/10.71568/DASDAGA2025.078","bibtex":"@inproceedings{Friesen_Meihost_Koch_Claes_Henning_2025, title={Estimation of piezoelectric material parameters under varying electric field conditions}, DOI={10.71568/DASDAGA2025.078}, author={Friesen, Olga and Meihost, Lars and Koch, Kevin and Claes, Leander and Henning, Bernd}, year={2025} }","short":"O. Friesen, L. Meihost, K. Koch, L. Claes, B. Henning, in: 2025.","mla":"Friesen, Olga, et al. Estimation of Piezoelectric Material Parameters under Varying Electric Field Conditions. 2025, doi:10.71568/DASDAGA2025.078."},"title":"Estimation of piezoelectric material parameters under varying electric field conditions","main_file_link":[{"open_access":"1"}],"conference":{"start_date":"2025-03-17","name":"DAS | DAGA 2025 - 51st Annual Meeting on Acoustics","location":"Copenhagen","end_date":"2025-03-20"},"doi":"10.71568/DASDAGA2025.078","oa":"1","date_updated":"2026-01-05T08:02:20Z","date_created":"2025-04-25T08:51:32Z","author":[{"first_name":"Olga","last_name":"Friesen","full_name":"Friesen, Olga","id":"44026"},{"first_name":"Lars","id":"24769","full_name":"Meihost, Lars","last_name":"Meihost"},{"full_name":"Koch, Kevin","last_name":"Koch","first_name":"Kevin"},{"first_name":"Leander","orcid":"0000-0002-4393-268X","last_name":"Claes","full_name":"Claes, Leander","id":"11829"},{"first_name":"Bernd","last_name":"Henning","full_name":"Henning, Bernd","id":"213"}],"status":"public","type":"conference","language":[{"iso":"eng"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"},{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"59689","user_id":"11829","department":[{"_id":"49"}]},{"user_id":"31496","_id":"63250","project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"language":[{"iso":"eng"}],"article_number":"192","publication":"Zeitschrift für angewandte Mathematik und Physik","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"Abstract\r\n \r\n An initial-boundary value problem for\r\n \r\n \r\n $$\\begin{aligned} \\left\\{ \\begin{array}{ll}u_{tt} = \\big (\\gamma (\\Theta ) u_{xt}\\big )_x + au_{xx} - \\big (f(\\Theta )\\big )_x, \\qquad & x\\in \\Omega , \\ t>0, \\\\[1mm] \\Theta _t = \\Theta _{xx} + \\gamma (\\Theta ) u_{xt}^2 - f(\\Theta ) u_{xt}, \\qquad & x\\in \\Omega , \\ t>0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n \r\n tt\r\n \r\n \r\n =\r\n \r\n (\r\n \r\n γ\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n u\r\n \r\n xt\r\n \r\n \r\n \r\n \r\n )\r\n \r\n x\r\n \r\n +\r\n a\r\n \r\n u\r\n \r\n xx\r\n \r\n \r\n -\r\n \r\n (\r\n \r\n f\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n \r\n )\r\n \r\n x\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n x\r\n ∈\r\n Ω\r\n ,\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n [\r\n 1\r\n m\r\n m\r\n ]\r\n \r\n \r\n Θ\r\n t\r\n \r\n =\r\n \r\n Θ\r\n \r\n xx\r\n \r\n \r\n +\r\n γ\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n u\r\n \r\n xt\r\n \r\n 2\r\n \r\n -\r\n f\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n u\r\n \r\n xt\r\n \r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n x\r\n ∈\r\n Ω\r\n ,\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered in an open bounded real interval\r\n \r\n \r\n $$\\Omega $$\r\n \r\n Ω\r\n \r\n \r\n \r\n . Under the assumption that\r\n \r\n \r\n $$\\gamma \\in C^0([0,\\infty ))$$\r\n \r\n \r\n γ\r\n ∈\r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n and\r\n \r\n \r\n $$f\\in C^0([0,\\infty ))$$\r\n \r\n \r\n f\r\n ∈\r\n \r\n C\r\n 0\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n are such that\r\n \r\n \r\n $$f(0)=0$$\r\n \r\n \r\n f\r\n (\r\n 0\r\n )\r\n =\r\n 0\r\n \r\n \r\n \r\n \r\n , and\r\n \r\n \r\n $$k_\\gamma \\le \\gamma \\le K_\\gamma $$\r\n \r\n \r\n \r\n k\r\n γ\r\n \r\n ≤\r\n γ\r\n ≤\r\n \r\n K\r\n γ\r\n \r\n \r\n \r\n \r\n \r\n as well as\r\n \r\n \r\n $$\\begin{aligned} |f(\\xi )| \\le K_f \\cdot (\\xi +1)^\\alpha \\qquad \\hbox {for all } \\xi \\ge 0 \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n |\r\n f\r\n \r\n (\r\n ξ\r\n )\r\n \r\n |\r\n \r\n ≤\r\n \r\n K\r\n f\r\n \r\n ·\r\n \r\n \r\n (\r\n ξ\r\n +\r\n 1\r\n )\r\n \r\n α\r\n \r\n \r\n for all\r\n \r\n ξ\r\n ≥\r\n 0\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n with some\r\n \r\n \r\n $$k_\\gamma>0, K_\\gamma>0, K_f>0$$\r\n \r\n \r\n \r\n k\r\n γ\r\n \r\n >\r\n 0\r\n ,\r\n \r\n K\r\n γ\r\n \r\n >\r\n 0\r\n ,\r\n \r\n K\r\n f\r\n \r\n >\r\n 0\r\n \r\n \r\n \r\n \r\n and\r\n \r\n \r\n $$\\alpha <\\frac{3}{2}$$\r\n \r\n \r\n α\r\n <\r\n \r\n 3\r\n 2\r\n \r\n \r\n \r\n \r\n \r\n , for all suitably regular initial data of arbitrary size a statement on global existence of a global weak solution is derived. By particularly covering the thermodynamically consistent choice\r\n \r\n \r\n $$f\\equiv id$$\r\n \r\n \r\n f\r\n ≡\r\n i\r\n d\r\n \r\n \r\n \r\n \r\n of predominant physical relevance, this appears to go beyond previous related literature which seems to either rely on independence of\r\n \r\n \r\n $$\\gamma $$\r\n \r\n γ\r\n \r\n \r\n \r\n on\r\n \r\n \r\n $$\\Theta $$\r\n \r\n Θ\r\n \r\n \r\n \r\n , or to operate on finite time intervals.\r\n "}],"volume":76,"author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T19:03:19Z","publisher":"Springer Science and Business Media LLC","date_updated":"2026-04-23T12:20:44Z","doi":"10.1007/s00033-025-02582-y","title":"Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities","issue":"5","publication_identifier":{"issn":["0044-2275","1420-9039"]},"publication_status":"published","intvolume":" 76","citation":{"ama":"Winkler M. Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities. Zeitschrift für angewandte Mathematik und Physik. 2025;76(5). doi:10.1007/s00033-025-02582-y","ieee":"M. Winkler, “Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities,” Zeitschrift für angewandte Mathematik und Physik, vol. 76, no. 5, Art. no. 192, 2025, doi: 10.1007/s00033-025-02582-y.","chicago":"Winkler, Michael. “Large-Data Solutions in One-Dimensional Thermoviscoelasticity Involving Temperature-Dependent Viscosities.” Zeitschrift Für Angewandte Mathematik Und Physik 76, no. 5 (2025). https://doi.org/10.1007/s00033-025-02582-y.","mla":"Winkler, Michael. “Large-Data Solutions in One-Dimensional Thermoviscoelasticity Involving Temperature-Dependent Viscosities.” Zeitschrift Für Angewandte Mathematik Und Physik, vol. 76, no. 5, 192, Springer Science and Business Media LLC, 2025, doi:10.1007/s00033-025-02582-y.","short":"M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 76 (2025).","bibtex":"@article{Winkler_2025, title={Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities}, volume={76}, DOI={10.1007/s00033-025-02582-y}, number={5192}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }","apa":"Winkler, M. (2025). Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities. Zeitschrift Für Angewandte Mathematik Und Physik, 76(5), Article 192. https://doi.org/10.1007/s00033-025-02582-y"},"year":"2025"},{"date_created":"2025-12-18T19:02:51Z","author":[{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"volume":25,"date_updated":"2026-04-23T12:19:51Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s00028-025-01144-z","title":"Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities","issue":"4","publication_status":"published","publication_identifier":{"issn":["1424-3199","1424-3202"]},"citation":{"chicago":"Winkler, Michael. “Large-Data Regular Solutions in a One-Dimensional Thermoviscoelastic Evolution Problem Involving Temperature-Dependent Viscosities.” Journal of Evolution Equations 25, no. 4 (2025). https://doi.org/10.1007/s00028-025-01144-z.","ieee":"M. Winkler, “Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities,” Journal of Evolution Equations, vol. 25, no. 4, Art. no. 108, 2025, doi: 10.1007/s00028-025-01144-z.","ama":"Winkler M. Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities. Journal of Evolution Equations. 2025;25(4). doi:10.1007/s00028-025-01144-z","apa":"Winkler, M. (2025). Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities. Journal of Evolution Equations, 25(4), Article 108. https://doi.org/10.1007/s00028-025-01144-z","mla":"Winkler, Michael. “Large-Data Regular Solutions in a One-Dimensional Thermoviscoelastic Evolution Problem Involving Temperature-Dependent Viscosities.” Journal of Evolution Equations, vol. 25, no. 4, 108, Springer Science and Business Media LLC, 2025, doi:10.1007/s00028-025-01144-z.","short":"M. Winkler, Journal of Evolution Equations 25 (2025).","bibtex":"@article{Winkler_2025, title={Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities}, volume={25}, DOI={10.1007/s00028-025-01144-z}, number={4108}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }"},"intvolume":" 25","year":"2025","user_id":"31496","project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"_id":"63249","language":[{"iso":"eng"}],"article_number":"108","type":"journal_article","publication":"Journal of Evolution Equations","status":"public","abstract":[{"text":"Abstract\r\n \r\n The model\r\n \r\n \r\n $$\\begin{aligned} \\left\\{ \\begin{array}{l}u_{tt} = \\big (\\gamma (\\Theta ) u_{xt}\\big )_x + au_{xx} - \\big (f(\\Theta )\\big )_x, \\\\[1mm] \\Theta _t = \\Theta _{xx} + \\gamma (\\Theta ) u_{xt}^2 - f(\\Theta ) u_{xt}, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n \r\n tt\r\n \r\n \r\n =\r\n \r\n (\r\n \r\n γ\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n u\r\n \r\n xt\r\n \r\n \r\n \r\n \r\n )\r\n \r\n x\r\n \r\n +\r\n a\r\n \r\n u\r\n \r\n xx\r\n \r\n \r\n -\r\n \r\n (\r\n \r\n f\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n \r\n )\r\n \r\n x\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n [\r\n 1\r\n m\r\n m\r\n ]\r\n \r\n \r\n Θ\r\n t\r\n \r\n =\r\n \r\n Θ\r\n \r\n xx\r\n \r\n \r\n +\r\n γ\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n u\r\n \r\n xt\r\n \r\n 2\r\n \r\n -\r\n f\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n u\r\n \r\n xt\r\n \r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n for thermoviscoelastic evolution in one-dimensional Kelvin–Voigt materials is considered. By means of an approach based on maximal Sobolev regularity theory of scalar parabolic equations, it is shown that if\r\n \r\n \r\n $$\\gamma _0>0$$\r\n \r\n \r\n \r\n γ\r\n 0\r\n \r\n >\r\n 0\r\n \r\n \r\n \r\n \r\n is fixed, then there exists\r\n \r\n \r\n $$\\delta =\\delta (\\gamma _0)>0$$\r\n \r\n \r\n δ\r\n =\r\n δ\r\n (\r\n \r\n γ\r\n 0\r\n \r\n )\r\n >\r\n 0\r\n \r\n \r\n \r\n \r\n with the property that for suitably regular initial data of arbitrary size an associated initial boundary value problem posed in an open bounded interval admits a global classical solution whenever\r\n \r\n \r\n $$\\gamma \\in C^2([0,\\infty ))$$\r\n \r\n \r\n γ\r\n ∈\r\n \r\n C\r\n 2\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n and\r\n \r\n \r\n $$f\\in C^2([0,\\infty ))$$\r\n \r\n \r\n f\r\n ∈\r\n \r\n C\r\n 2\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n are such that\r\n \r\n \r\n $$f(0)=0$$\r\n \r\n \r\n f\r\n (\r\n 0\r\n )\r\n =\r\n 0\r\n \r\n \r\n \r\n \r\n and\r\n \r\n \r\n $$|f(\\xi )| \\le K_f \\cdot (\\xi +1)^\\alpha $$\r\n \r\n \r\n \r\n |\r\n f\r\n \r\n (\r\n ξ\r\n )\r\n \r\n |\r\n \r\n ≤\r\n \r\n K\r\n f\r\n \r\n ·\r\n \r\n \r\n (\r\n ξ\r\n +\r\n 1\r\n )\r\n \r\n α\r\n \r\n \r\n \r\n \r\n \r\n for all\r\n \r\n \r\n $$\\xi \\ge 0$$\r\n \r\n \r\n ξ\r\n ≥\r\n 0\r\n \r\n \r\n \r\n \r\n and some\r\n \r\n \r\n $$K_f>0$$\r\n \r\n \r\n \r\n K\r\n f\r\n \r\n >\r\n 0\r\n \r\n \r\n \r\n \r\n and\r\n \r\n \r\n $$\\alpha <\\frac{3}{2}$$\r\n \r\n \r\n α\r\n <\r\n \r\n 3\r\n 2\r\n \r\n \r\n \r\n \r\n \r\n , and that\r\n \r\n \r\n $$\\begin{aligned} \\gamma _0 \\le \\gamma (\\xi ) \\le \\gamma _0 + \\delta \\qquad \\hbox {for all } \\xi \\ge 0. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n γ\r\n 0\r\n \r\n ≤\r\n γ\r\n \r\n (\r\n ξ\r\n )\r\n \r\n ≤\r\n \r\n γ\r\n 0\r\n \r\n +\r\n δ\r\n \r\n for all\r\n \r\n ξ\r\n ≥\r\n 0\r\n .\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n This is supplemented by a statement on global existence of certain strong solutions, particularly continuous in both components, under weaker conditions on the initial data.\r\n ","lang":"eng"}]},{"year":"2025","citation":{"apa":"Winkler, M. (2025). Rough solutions in one-dimensional nonlinear thermoelasticity. Calculus of Variations and Partial Differential Equations, 65(1), Article 1. https://doi.org/10.1007/s00526-025-03170-8","short":"M. Winkler, Calculus of Variations and Partial Differential Equations 65 (2025).","bibtex":"@article{Winkler_2025, title={Rough solutions in one-dimensional nonlinear thermoelasticity}, volume={65}, DOI={10.1007/s00526-025-03170-8}, number={11}, journal={Calculus of Variations and Partial Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }","mla":"Winkler, Michael. “Rough Solutions in One-Dimensional Nonlinear Thermoelasticity.” Calculus of Variations and Partial Differential Equations, vol. 65, no. 1, 1, Springer Science and Business Media LLC, 2025, doi:10.1007/s00526-025-03170-8.","ieee":"M. Winkler, “Rough solutions in one-dimensional nonlinear thermoelasticity,” Calculus of Variations and Partial Differential Equations, vol. 65, no. 1, Art. no. 1, 2025, doi: 10.1007/s00526-025-03170-8.","chicago":"Winkler, Michael. “Rough Solutions in One-Dimensional Nonlinear Thermoelasticity.” Calculus of Variations and Partial Differential Equations 65, no. 1 (2025). https://doi.org/10.1007/s00526-025-03170-8.","ama":"Winkler M. Rough solutions in one-dimensional nonlinear thermoelasticity. Calculus of Variations and Partial Differential Equations. 2025;65(1). doi:10.1007/s00526-025-03170-8"},"intvolume":" 65","publication_status":"published","publication_identifier":{"issn":["0944-2669","1432-0835"]},"issue":"1","title":"Rough solutions in one-dimensional nonlinear thermoelasticity","doi":"10.1007/s00526-025-03170-8","publisher":"Springer Science and Business Media LLC","date_updated":"2026-04-23T12:18:59Z","author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-18T19:01:02Z","volume":65,"abstract":[{"lang":"eng","text":"Abstract\r\n \r\n The hyperbolic-parabolic model\r\n \r\n \r\n $$\\begin{aligned} \\left\\{ \\begin{array}{ll} u_{tt} = u_{xx} - \\big (f(\\Theta )\\big )_x, \\qquad & x\\in \\Omega , \\ t>0, \\\\ \\Theta _t = \\Theta _{xx} - f(\\Theta ) u_{xt}, \\qquad & x\\in \\Omega , \\ t>0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n \r\n tt\r\n \r\n \r\n =\r\n \r\n u\r\n \r\n xx\r\n \r\n \r\n -\r\n \r\n (\r\n \r\n f\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n \r\n )\r\n \r\n x\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n x\r\n ∈\r\n Ω\r\n ,\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n Θ\r\n t\r\n \r\n =\r\n \r\n Θ\r\n \r\n xx\r\n \r\n \r\n -\r\n f\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n u\r\n \r\n xt\r\n \r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n x\r\n ∈\r\n Ω\r\n ,\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n for the evolution of the displacement variable\r\n u\r\n and the temperature\r\n \r\n \r\n $$\\Theta \\ge 0$$\r\n \r\n \r\n Θ\r\n ≥\r\n 0\r\n \r\n \r\n \r\n \r\n during thermoelastic interaction in a one-dimensional bounded interval\r\n \r\n \r\n $$\\Omega $$\r\n \r\n Ω\r\n \r\n \r\n \r\n is considered. Whereas the literature has provided comprehensive results on global solutions for sufficiently regular initial data\r\n \r\n \r\n $$(u_0,u_{0t},\\Theta _0)=(u,u_t,\\Theta )|_{t=0}$$\r\n \r\n \r\n \r\n (\r\n \r\n u\r\n 0\r\n \r\n ,\r\n \r\n u\r\n \r\n 0\r\n t\r\n \r\n \r\n ,\r\n \r\n Θ\r\n 0\r\n \r\n )\r\n \r\n =\r\n \r\n (\r\n u\r\n ,\r\n \r\n u\r\n t\r\n \r\n ,\r\n Θ\r\n )\r\n \r\n \r\n \r\n |\r\n \r\n \r\n t\r\n =\r\n 0\r\n \r\n \r\n \r\n \r\n \r\n \r\n when\r\n \r\n \r\n $$f\\equiv id$$\r\n \r\n \r\n f\r\n ≡\r\n i\r\n d\r\n \r\n \r\n \r\n \r\n , it seems to have remained open so far how far a solution theory can be built solely on the two fundamental physical principles of energy conservation and entropy nondecrease. The present manuscript addresses this by asserting global existence of weak solutions under assumptions which are energy- and entropy-minimal in the sense of allowing for any initial data\r\n \r\n \r\n $$u_0\\in W_0^{1,2}(\\Omega )$$\r\n \r\n \r\n \r\n u\r\n 0\r\n \r\n ∈\r\n \r\n W\r\n 0\r\n \r\n 1\r\n ,\r\n 2\r\n \r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n \r\n \r\n ,\r\n \r\n \r\n $$u_{0t} \\in L^2(\\Omega )$$\r\n \r\n \r\n \r\n u\r\n \r\n 0\r\n t\r\n \r\n \r\n ∈\r\n \r\n L\r\n 2\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n \r\n \r\n and\r\n \r\n \r\n $$0\\le \\Theta _0\\in L^1(\\Omega )$$\r\n \r\n \r\n 0\r\n ≤\r\n \r\n Θ\r\n 0\r\n \r\n ∈\r\n \r\n L\r\n 1\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n \r\n \r\n , and which apply to arbitrary\r\n \r\n \r\n $$f\\in C^1([0,\\infty ))$$\r\n \r\n \r\n f\r\n ∈\r\n \r\n C\r\n 1\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n \r\n \r\n \r\n with\r\n \r\n \r\n $$f(0)=0$$\r\n \r\n \r\n f\r\n (\r\n 0\r\n )\r\n =\r\n 0\r\n \r\n \r\n \r\n \r\n and\r\n \r\n \r\n $$f'>0$$\r\n \r\n \r\n \r\n f\r\n ′\r\n \r\n >\r\n 0\r\n \r\n \r\n \r\n \r\n on\r\n \r\n \r\n $$[0,\\infty )$$\r\n \r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n \r\n \r\n \r\n .\r\n "}],"status":"public","type":"journal_article","publication":"Calculus of Variations and Partial Differential Equations","article_number":"1","language":[{"iso":"eng"}],"project":[{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"_id":"63246","user_id":"31496"},{"date_created":"2024-05-02T13:25:29Z","title":"Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last","year":"2024","language":[{"iso":"ger"}],"ddc":["620"],"publication":"Fortschritte der Akustik - DAGA 2024","file":[{"content_type":"application/pdf","relation":"main_file","creator":"ofriesen","date_created":"2024-05-02T13:38:37Z","date_updated":"2024-05-02T14:07:24Z","file_id":"53826","access_level":"open_access","file_name":"daga2024friesen.pdf","file_size":453108}],"abstract":[{"lang":"ger","text":"Piezoelektrische Keramiken finden sowohl in Sensoren als auch in Aktoren Anwendung. Bei Hochleistungs-Ultraschallanwendungen sind diese Komponenten erheblichen elektrischen und mechanischen Belastungen ausgesetzt, was zum Auftreten nichtlinearer Effekte führt. Um das nichtlineare Materialverhalten piezoelektrischer Keramiken zu charakterisieren, kann eine statische mechanische Last aufgebracht werden, die den mechanischen Arbeitspunkt verschiebt. Durch Variation dieser statischen mechanischen Belastung kann das lineare Verhalten in jedem Betriebspunkt charakterisiert werden, woraufhin die nichtlinearen Eigenschaften des Materials angenähert werden können. Allerdings ist die Sicherstellung einer homogenen mechanischen Last anspruchsvoll. Alternativ kann eine hydrostatische Belastung realisiert werden, indem die Probe in einen Behälter gegeben wird, der mit unter Druck stehendem Fluid gefüllt ist. Dadurch wird eine gleichmäßige Lastverteilung über die Oberfläche der Probe erreicht.\r\n\r\nIn diesem Beitrag wird ein Versuchsaufbau zur Durchführung elektrischer Impedanzmessungen an piezoelektrischen Keramiken in einem Druckbehälter vorgestellt. Die Probe wird im Inneren des Druckbehälters elektrisch kontaktiert. Unter Verwendung von unter Druck stehendem Argon wird auf diese Weise die Messung der elektrischen Impedanz unter hydrostatischer Last von bis zu 200 bar ermöglicht. Anschließend wird ein inverses Verfahren angewendet, um die Materialparameter in Abhängigkeit von der aufgebrachten Last zu ermitteln."}],"author":[{"last_name":"Friesen","full_name":"Friesen, Olga","id":"44026","first_name":"Olga"},{"last_name":"Pasha","full_name":"Pasha, Muhammad Ahsan","first_name":"Muhammad Ahsan"},{"last_name":"Schwengelbeck","full_name":"Schwengelbeck, Max","first_name":"Max"},{"id":"11829","full_name":"Claes, Leander","orcid":"0000-0002-4393-268X","last_name":"Claes","first_name":"Leander"},{"first_name":"Elmar","id":"15164","full_name":"Baumhögger, Elmar","last_name":"Baumhögger"},{"last_name":"Henning","id":"213","full_name":"Henning, Bernd","first_name":"Bernd"}],"date_updated":"2026-01-05T07:56:21Z","oa":"1","conference":{"location":"Hannover","end_date":"2024-03-21","start_date":"2024-03-18","name":"DAGA 2024 - 50. JAHRESTAGUNG FÜR AKUSTIK"},"has_accepted_license":"1","publication_status":"published","page":"1117–1120","citation":{"bibtex":"@inproceedings{Friesen_Pasha_Schwengelbeck_Claes_Baumhögger_Henning_2024, title={Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last}, booktitle={Fortschritte der Akustik - DAGA 2024}, author={Friesen, Olga and Pasha, Muhammad Ahsan and Schwengelbeck, Max and Claes, Leander and Baumhögger, Elmar and Henning, Bernd}, year={2024}, pages={1117–1120} }","short":"O. Friesen, M.A. Pasha, M. Schwengelbeck, L. Claes, E. Baumhögger, B. Henning, in: Fortschritte der Akustik - DAGA 2024, 2024, pp. 1117–1120.","mla":"Friesen, Olga, et al. “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last.” Fortschritte der Akustik - DAGA 2024, 2024, pp. 1117–1120.","apa":"Friesen, O., Pasha, M. A., Schwengelbeck, M., Claes, L., Baumhögger, E., & Henning, B. (2024). Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last. Fortschritte der Akustik - DAGA 2024, 1117–1120.","chicago":"Friesen, Olga, Muhammad Ahsan Pasha, Max Schwengelbeck, Leander Claes, Elmar Baumhögger, and Bernd Henning. “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last.” In Fortschritte der Akustik - DAGA 2024, 1117–1120, 2024.","ieee":"O. Friesen, M. A. Pasha, M. Schwengelbeck, L. Claes, E. Baumhögger, and B. Henning, “Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last,” in Fortschritte der Akustik - DAGA 2024, Hannover, 2024, pp. 1117–1120.","ama":"Friesen O, Pasha MA, Schwengelbeck M, Claes L, Baumhögger E, Henning B. Untersuchung piezoelektrischer Materialeigenschaften unter hydrostatischer Last. In: Fortschritte der Akustik - DAGA 2024. ; 2024:1117–1120."},"user_id":"11829","_id":"53822","project":[{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"file_date_updated":"2024-05-02T14:07:24Z","type":"conference","status":"public"},{"has_accepted_license":"1","year":"2024","page":"1113–1116","citation":{"chicago":"Koch, Kevin, Leander Claes, Benjamin Jurgelucks, Lars Meihost, and Bernd Henning. “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze.” In Fortschritte der Akustik - DAGA 2024, edited by Deutsche Gesellschaft für Akustik e.V., 1113–1116, 2024.","ieee":"K. Koch, L. Claes, B. Jurgelucks, L. Meihost, and B. Henning, “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze,” in Fortschritte der Akustik - DAGA 2024, 2024, pp. 1113–1116.","ama":"Koch K, Claes L, Jurgelucks B, Meihost L, Henning B. Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze. In: Gesellschaft für Akustik e.V. D, ed. Fortschritte der Akustik - DAGA 2024. ; 2024:1113–1116.","short":"K. Koch, L. Claes, B. Jurgelucks, L. Meihost, B. Henning, in: D. Gesellschaft für Akustik e.V. (Ed.), Fortschritte der Akustik - DAGA 2024, 2024, pp. 1113–1116.","bibtex":"@inproceedings{Koch_Claes_Jurgelucks_Meihost_Henning_2024, title={Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze}, booktitle={Fortschritte der Akustik - DAGA 2024}, author={Koch, Kevin and Claes, Leander and Jurgelucks, Benjamin and Meihost, Lars and Henning, Bernd}, editor={Gesellschaft für Akustik e.V., Deutsche }, year={2024}, pages={1113–1116} }","mla":"Koch, Kevin, et al. “Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze.” Fortschritte der Akustik - DAGA 2024, edited by Deutsche Gesellschaft für Akustik e.V., 2024, pp. 1113–1116.","apa":"Koch, K., Claes, L., Jurgelucks, B., Meihost, L., & Henning, B. (2024). Inverses Verfahren zur Identifikation piezoelektrischer Materialparameter unterstützt durch neuronale Netze. In D. Gesellschaft für Akustik e.V. 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