A regularized semigroup for a Lebowitz–Rubinow's model.

In this Note, we complete [1] and we study the Lebowitz–Rubinow''s model with the biological law of perfect memory. In this model, each cell is characterized by its cell cycle length <f>l</f> (<f>0&les;l1<l<l2<∞</f>) and its age <f>a</f> (<f>0<a<l</f>). If <f>l1>0</f>, a complete study of this model can be found in [1]. Here we show that if <f>l1=0</f> then this model becomes ill-posed. We use the theory of generalized semigroups to remedy to this model. To cite this article: M. Boulanouar, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 865–868. [Copyright &y& Elsevier]