Hereditary Evolution Processes Under Impulsive Effects

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Abstract
In this note, we deal with a model of population dynamics with memory effects subject to instantaneous external actions. We interpret the model as an impulsive Cauchy problem driven by a semilinear differential equation with functional delay. The existence of delayed impulsive solutions to the Cauchy problem leads to the presence of hereditary impulsive dynamics for the model. Furthermore, using the same procedure we study a nonlinear reaction–diffusion model.
Funding Information
  • Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (2019, 2019)
  • Università degli Studi di Perugia (2018, 2018)

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