Baza Publikacji Pracowników Politechniki Lubelskiej

Status:
Autorzy:	Bobrowski Adam, Morawska Katarzyna
Rok wydania:	2012
Wersja dokumentu:	Drukowana \| Elektroniczna
Język:	angielski
Numer czasopisma:	7
Wolumen/Tom:	17
Strony:	2313 - 2327
Impact Factor:	0,88
Web of Science® Times Cited:	21
Scopus® Cytowania:	25
Bazy:	Web of Science \| Scopus
Efekt badań statutowych	NIE
Materiał konferencyjny:	NIE
Publikacja OA:	NIE
Abstrakty:	angielski
	We provide a link between two recent models of dynamics of synaptic depression. To this end, we specify the missing transmission conditions in the PDE model of Bielecki and Kalita, and show that if diusion is fast and communication between pools is slow, the PDE model is well approximated by the ODE model of Aristizabal and Glavinovic. From the mathematical point of view the ODE model is obtained as a singular perturbation of the PDE model with singularities both in the operator and in the boundary and transmission conditions. The result is put in the context of degenerate convergence of semigroups of operators, where a sequence of strongly continuous semigroups approaches a semigroup that is strongly continuous only on a subspace of the original Banach space. Biologically, our approach allows a new, natural interpretation of the ODE model's parameters.

From a PDE model to an ODE model of dynamics of synaptic depression