[{"doi":"10.1007/s00245-025-10243-9","title":"Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters","author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-04-02T11:23:25Z","volume":91,"date_updated":"2026-02-26T15:59:30Z","publisher":"Springer Science and Business Media LLC","citation":{"chicago":"Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters.” Applied Mathematics & Optimization 91, no. 2 (2025). https://doi.org/10.1007/s00245-025-10243-9.","ieee":"M. Winkler, “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters,” Applied Mathematics & Optimization, vol. 91, no. 2, Art. no. 44, 2025, doi: 10.1007/s00245-025-10243-9.","ama":"Winkler M. Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters. Applied Mathematics & Optimization. 2025;91(2). doi:10.1007/s00245-025-10243-9","short":"M. Winkler, Applied Mathematics & Optimization 91 (2025).","bibtex":"@article{Winkler_2025, title={Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}, volume={91}, DOI={10.1007/s00245-025-10243-9}, number={244}, journal={Applied Mathematics & Optimization}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }","mla":"Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters.” Applied Mathematics & Optimization, vol. 91, no. 2, 44, Springer Science and Business Media LLC, 2025, doi:10.1007/s00245-025-10243-9.","apa":"Winkler, M. (2025). Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters. Applied Mathematics & Optimization, 91(2), Article 44. https://doi.org/10.1007/s00245-025-10243-9"},"intvolume":" 91","year":"2025","issue":"2","publication_status":"published","publication_identifier":{"issn":["0095-4616","1432-0606"]},"language":[{"iso":"eng"}],"article_number":"44","user_id":"11829","department":[{"_id":"90"}],"project":[{"_id":"245","name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)"}],"_id":"59258","status":"public","type":"journal_article","publication":"Applied Mathematics & Optimization"},{"intvolume":" 91","citation":{"ieee":"M. Winkler, “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters,” Applied Mathematics & Optimization, vol. 91, no. 2, Art. no. 44, 2025, doi: 10.1007/s00245-025-10243-9.","chicago":"Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters.” Applied Mathematics & Optimization 91, no. 2 (2025). https://doi.org/10.1007/s00245-025-10243-9.","ama":"Winkler M. Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters. Applied Mathematics & Optimization. 2025;91(2). doi:10.1007/s00245-025-10243-9","mla":"Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters.” Applied Mathematics & Optimization, vol. 91, no. 2, 44, Springer Science and Business Media LLC, 2025, doi:10.1007/s00245-025-10243-9.","bibtex":"@article{Winkler_2025, title={Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}, volume={91}, DOI={10.1007/s00245-025-10243-9}, number={244}, journal={Applied Mathematics & Optimization}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }","short":"M. Winkler, Applied Mathematics & Optimization 91 (2025).","apa":"Winkler, M. (2025). Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters. Applied Mathematics & Optimization, 91(2), Article 44. https://doi.org/10.1007/s00245-025-10243-9"},"year":"2025","issue":"2","publication_identifier":{"issn":["0095-4616","1432-0606"]},"publication_status":"published","doi":"10.1007/s00245-025-10243-9","title":"Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters","volume":91,"author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T20:20:06Z","date_updated":"2025-12-18T20:20:16Z","publisher":"Springer Science and Business Media LLC","status":"public","abstract":[{"text":"Abstract\r\n A Neumann-type initial-boundary value problem for \r\n \r\n $$\\begin{aligned} \\left\\{ \\begin{array}{l} u_{tt} = \\nabla \\cdot (\\gamma (\\Theta ) \\nabla u_t) + a \\nabla \\cdot (\\gamma (\\Theta ) \\nabla u) + \\nabla \\cdot f(\\Theta ), \\\\ \\Theta _t = D\\Delta \\Theta + \\Gamma (\\Theta ) |\\nabla u_t|^2 + F(\\Theta )\\cdot \\nabla u_t, \\end{array} \\right. \\end{aligned}$$\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 (\r\n γ\r\n \r\n (\r\n Θ\r\n )\r\n \r\n ∇\r\n \r\n u\r\n t\r\n \r\n )\r\n \r\n +\r\n a\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 \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 \r\n \r\n \r\n \r\n \r\n Θ\r\n t\r\n \r\n =\r\n D\r\n Δ\r\n Θ\r\n +\r\n Γ\r\n \r\n (\r\n Θ\r\n )\r\n \r\n \r\n \r\n |\r\n ∇\r\n \r\n u\r\n t\r\n \r\n |\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 ∇\r\n \r\n u\r\n t\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 a smoothly bounded domain \r\n \r\n $$\\Omega \\subset \\mathbb {R}^n$$\r\n \r\n \r\n Ω\r\n ⊂\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n \r\n \r\n \r\n , \r\n \r\n $$n\\ge 1$$\r\n \r\n \r\n n\r\n ≥\r\n 1\r\n \r\n \r\n \r\n . In the case when \r\n \r\n $$n=1$$\r\n \r\n \r\n n\r\n =\r\n 1\r\n \r\n \r\n \r\n , \r\n \r\n $$\\gamma \\equiv \\Gamma $$\r\n \r\n \r\n γ\r\n ≡\r\n Γ\r\n \r\n \r\n \r\n and \r\n \r\n $$f\\equiv F$$\r\n \r\n \r\n f\r\n ≡\r\n F\r\n \r\n \r\n \r\n , this system coincides with the standard model for heat generation in a viscoelastic material of Kelvin-Voigt type, well-understood in situations in which \r\n \r\n $$\\gamma =const$$\r\n \r\n \r\n γ\r\n =\r\n c\r\n o\r\n n\r\n s\r\n t\r\n \r\n \r\n \r\n . Covering scenarios in which all key ingredients \r\n \r\n $$\\gamma ,\\Gamma ,f$$\r\n \r\n \r\n γ\r\n ,\r\n Γ\r\n ,\r\n f\r\n \r\n \r\n \r\n and F may depend on the temperature \r\n \r\n $$\\Theta $$\r\n \r\n Θ\r\n \r\n \r\n here, for initial data which merely satisfy \r\n \r\n $$u_0\\in W^{1,p+2}(\\Omega )$$\r\n \r\n \r\n \r\n u\r\n 0\r\n \r\n ∈\r\n \r\n W\r\n \r\n 1\r\n ,\r\n p\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 $$u_{0t}\\in W^{1,p}(\\Omega )$$\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 W\r\n \r\n 1\r\n ,\r\n p\r\n \r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n \r\n and \r\n \r\n $$\\Theta _0\\in W^{1,p}(\\Omega )$$\r\n \r\n \r\n \r\n Θ\r\n 0\r\n \r\n ∈\r\n \r\n W\r\n \r\n 1\r\n ,\r\n p\r\n \r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n \r\n with some \r\n \r\n $$p\\ge 2$$\r\n \r\n \r\n p\r\n ≥\r\n 2\r\n \r\n \r\n \r\n such that \r\n \r\n $$p>n$$\r\n \r\n \r\n p\r\n >\r\n n\r\n \r\n \r\n \r\n , a result on local-in-time existence and uniqueness is derived in a natural framework of weak solvability.","lang":"eng"}],"publication":"Applied Mathematics & Optimization","type":"journal_article","language":[{"iso":"eng"}],"article_number":"44","user_id":"31496","_id":"63344"}]