Abstract
The goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical biology: epidemiology, predator-prey interactions and oncology.
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Duprez, M., Perasso, A. Criterion of positivity for semilinear problems with applications in biology. Positivity 21, 1383–1392 (2017). https://doi.org/10.1007/s11117-017-0474-0
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DOI: https://doi.org/10.1007/s11117-017-0474-0