Measure differential equation with a nonlinear growth/decay term - Düll, Christian; Gwiazda, Piotr; Marciniak-Czochra, Anna; Skrzeczkowski, Jakub (Arxiv, 2021)
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.
Artikelversion vom 26. Oktober 2021
Gesehen am 09.01.2024