Measure differential equation with a nonlinear growth/decay term

• Verfasst von: Düll, Christian [VerfasserIn]
• Verfasst von: Gwiazda, Piotr [VerfasserIn]
• Verfasst von: Marciniak-Czochra, Anna [VerfasserIn]
• Verfasst von: Skrzeczkowski, Jakub [VerfasserIn]
• Titel: Measure differential equation with a nonlinear growth/decay term
• Verf.angabe: Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra, and Jakub Skrzeczkowski
• E-Jahr: 2021
• Jahr: 30 Sep 2021
• Umfang: 30 S.
• Fussnoten: Artikelversion vom 26. Oktober 2021 ; Gesehen am 09.01.2024
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [Erscheinungsort nicht ermittelbar] : Arxiv.org, 1991
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), Artikel-ID 2109.14987, Seite 1-30
• DOI: doi:10.48550/arXiv.2109.14987
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 35F25, 35R06
• Sach-SW: Mathematics - Analysis of PDEs
• K10plus-PPN: 1817211153

Abstract

We obtain an existence result for a Measure Differential Equation with an additional nonlinear growth/decay term that may change the sign. The proof requires a modification of approximating schemes proposed by Piccoli and Rossi. The new scheme combines model discretisation with the exponential solution of the nonlinear growth/decay and hence preserves nonnegativity of the measure. Furthermore, we formulate a simpler analytic condition on the Measure Vector Field which substantially simplifies the previous proof of continuity of solutions with respect to initial data.