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Dimension of measures invariant with respect to the Ważewska partial differential equation. (English) Zbl 1036.35054
Summary: We study asymptotic properties of a nonlinear first-order partial differential equation which describes the reproduction of blood cells. This equation under conditions proposed by Ważewska generates a semigroup of transformations with highly chaotic behaviour of trajectories. We show that this semigroup has invariant measures with arbitrary large dimension.

35F25Initial value problems for first order nonlinear PDE
35B40Asymptotic behavior of solutions of PDE
92C37Cell biology
Full Text: DOI
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