Measure differential equation with a nonlinear growth/decay term
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 solut...
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| Main Authors: | , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
30 Sep 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-30 |
| DOI: | 10.48550/arXiv.2109.14987 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.48550/arXiv.2109.14987 Verlag, kostenfrei, Volltext: http://arxiv.org/abs/2109.14987 
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| Author Notes: | Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra, and Jakub Skrzeczkowski |
| Summary: | 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. |
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| Item Description: | Artikelversion vom 26. Oktober 2021 Gesehen am 09.01.2024 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2109.14987 |