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Oscillation and global attractivity in a discrete survival red blood cells model

I. Kubiaczyk, S. H. Saker (2003)

Applicationes Mathematicae

We consider the discrete survival red blood cells model (*) N n + 1 - N = - δ N + P e - a N n - k , where δₙ and Pₙ are positive sequences. In the autonomous case we show that (*) has a unique positive steady state N*, we establish some sufficient conditions for oscillation of all positive solutions about N*, and when k = 1 we give a sufficient condition for N* to be globally asymptotically stable. In the nonatonomous case, assuming that there exists a positive solution Nₙ*, we present necessary and sufficient conditions for oscillation...

Oxygen exchange between multiple capillaries and living tissues: An homogenisation study

Andro Mikelić, Mario Primicerio (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A mathematical model for a problem of blood perfusion in a living tissue through a system of parallel capillaries is studied. Oxygen is assumed to be transported in two forms: freely diffusing and bounded (to erytrocytes in blood, to myoglobin in tissue). Existence of a weak solution is proved and a homogensation procedure is carried out in the case of randomly distribuited capillaries.

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