WELL-POSEDNESS OF A NONLINEAR MODEL OF PROLIFERATING CELL POPULATIONS WITH INHERITED CYCLE LENGTH

doi:10.1016/S0252-9602(16)30066-2

Abstract

Abstract:

This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow's model[16] discussed in[8, 9] modeling a proliferating age structured cell population with inherited properties. We give existence and uniqueness results on appropriate weighted L^p-spaces with 1≤p<∞ in the case where the rate of cells mortality σ and the transition rate k are depending on the total density of population. General local and nonlocal reproduction rules are considered.

Key words: evolution equation, local and nonlocal boundary conditions, quasi-accretive operators, mild solutions, strong solutions, local and global solutions

CLC Number:

47H06

Abdul-Majeed AL-IZERI, Khalid LATRACH. WELL-POSEDNESS OF A NONLINEAR MODEL OF PROLIFERATING CELL POPULATIONS WITH INHERITED CYCLE LENGTH[J].Acta mathematica scientia,Series B, 2016, 36(5): 1225-1244.

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