arXiv:1701.05314 Abstract | arXiv Analytics

arXiv:1701.05314 [math.AP]Abstract References Reviews Resources

Criterion of positivity for semilinear problems with applications in biology

Published 2017-01-19Version 1

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.

Comments: Accepted

Categories: math.AP, q-bio.QM

Subjects: 35A01, 35Q92, 92D25

Keywords: semilinear problem, applications, infinite dimensional semilinear abstract cauchy, dimensional semilinear abstract cauchy problems, positivity

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