Criterion of positivity for semilinear problems with applications in biology

DOI10.1007/S11117-017-0474-0zbMATH Open1516.35030arXiv1701.05314MaRDI QIDQ6282111

Publication date: 19 January 2017

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.

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Positive solutions to PDEs (35B09)

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