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Measure Differential Equation with a Nonlinear Growth/Decay Term
- Publication Year :
- 2021
-
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.<br />Comment: 25 pages + appendix + references
- Subjects :
- Mathematics - Analysis of PDEs
35F25, 35R06
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2109.14987
- Document Type :
- Working Paper