Well-posedness of a nonlinear model of proliferating cell populations with inherited cycle length

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• 作者：Abdul-Majeed AL-IZERI ^{Abdul_Majeed.Al_izeri@math.univ-bpclermont.fr" class="auth_mail" title="E-mail the corresponding author} ; Khalid LATRACH ; ^{Khalid.Latrach@math.univ-bpclermont.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：evolution equation ; local and nonlocal boundary conditions ; quasi-accretive operators ; mild solutions ; strong solutions ; local and global solutions
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：36
• 期：5
• 页码：1225-1244
• 全文大小：401 K

文摘

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.