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Marcello D'abbicco
Ruolo
Ricercatore a tempo determinato - tipo B
Organizzazione
Università degli Studi di Bari Aldo Moro
Dipartimento
DIPARTIMENTO DI MATEMATICA
Area Scientifica
AREA 01 - Scienze matematiche e informatiche
Settore Scientifico Disciplinare
MAT/05 - Analisi Matematica
Settore ERC 1° livello
Non Disponibile
Settore ERC 2° livello
Non Disponibile
Settore ERC 3° livello
Non Disponibile
We propose a system of first-order ordinary differential equations to describe and understand the physiological mechanisms of the interplay between plasma glucose and insulin and their behaviors in diabetes. The proposed model is based on Hill and step functions which are used to simulate the switch-like behavior that occurs in metabolic regulatory variables when some of the threshold parameters are approached. A simplified piece-wise linear system is also proposed to study the possible equilibria and solutions and used to introduce simple theoretical control mechanisms representing the action of an artificial pancreas and regulating exogenous insulin.
The authors study the Cauchy problem for the semi-linear damped wave equation in any space dimension. It is assumed that the time-dependent damping term is effective. The global existence of small energy data solutions for polynomial nonlinear term in the supercritical case is proved.
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