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Criterion of positivity for semilinear problems with applications in biology

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.

preprint2017arXivOpen access
Michel DuprezAntoine Perasso
math.APQuantitative Methods
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Michel DuprezAntoine Perasso

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