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Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2021

An integrated semigroup approach for age structured equations with diffusion and non-homogeneous boundary conditions

Résumé

In this work, we consider a linear age-structured problem with diffusion and non-homogeneous boundary conditions both for the age and the space variables. We handle this linear problem by rewriting it as a nondensely defined abstract Cauchy problem. To that aim we develop a new result on the closedness of a commutative sum of two non-densely defined operators by using the theory of integrated semigroups. As an application of this abstract result, we are able to associate a suitable integrated semigroup to some age-structured problem with spatial diffusion and equipped with non-homogeneous boundary conditions. This integrated semigroup is characterized by the description of its infinitesimal generator. Further applications of our abstract result are also given to the commutative sum of two almost sectorial operators, for which we derive a closedness results.
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Dates et versions

hal-03161177 , version 1 (05-03-2021)
hal-03161177 , version 2 (02-12-2021)

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Arnaud Ducrot, Pierre Magal, Alexandre Thorel. An integrated semigroup approach for age structured equations with diffusion and non-homogeneous boundary conditions. Nonlinear Differential Equations and Applications, 2021, 28 (5), pp.49. ⟨10.1007/s00030-021-00710-x⟩. ⟨hal-03161177v2⟩
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