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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.

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